The mass of the ball is 6.67 kg
Explanation:
The momentum of an object is given by:
[tex]p=mv[/tex]
where
p is the momentum
m is the mass of the object
v is its velocity
It must be noted that momentum is a vector quantity, so it has both magnitude and direction (but here only the magnitude is given).
For the ball in this problem, we have:
v = 1.5 m/s is its velocity
p = 10.0 kg m/s is its momentum
Solving the formula for m, we find the mass of the ball:
[tex]m=\frac{p}{v}=\frac{10}{1.5}=6.67 kg[/tex]
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The force on a particle of mass m is given by F=26i-12t2j where F is in N and in s. What
will be the change in the particle’s momentum between 1.0s and 2.0s
Answer:
26i-28j
Explanation:
Mathematically, rate of change of something with respect to another is obtained through the operation called differentiation. Integration is the reverse process of differentiation.
We know that force is the rate of change of momentum.
that is,
F=[tex]\frac{dP}{dt}[/tex]
where,
P=momentum
t=time
dP=small change in momentum
dt=small change in time
dP=Fdt (multiplying both sides with dt)
To get change of momentum within a particular time interval, we have to integrate the above expression giving the necessary limits according to the problem.
Here, we have to calculate the change in momentum between 1.0s and 2.0s. So, the limit of integration is 1.0 to 2.0.
Thus,
[tex]\int\limits^P_p {} \, dP[/tex]=[tex]\int\limits^2_1 {F} \, dt[/tex]
where,
p=momentum at t=1s
P=momentum at t=2s
substituting F in the above equation,
[tex]\int\limits^P_p {} \, dP[/tex]=[tex]\int\limits^2_1 {26i-12jt^{2}} \, dt[/tex]
[tex]\int\limits^P_p {} \, dP[/tex] = P-p = Change in momentum between 1.0s and 2.0s
[tex]\int\limits^2_1 {26i-12jt^{2}} \, dt[/tex] = [tex]\int\limits^2_1 {26i} \, dt - \int\limits^2_1 {12t^{2}j } \, dt[/tex] (Since we can integrate each term of an expression separately)
[tex]\int\limits^2_1 {26i} \, dt - \int\limits^2_1 {12t^{2}j } \, dt[/tex] = [tex]26i(2-1) - 12j(\frac{2^{3} -1^{3} }{3} )[/tex]
=26i-28j
therefore the change in momentum between 1.0s and 2.0s is 26i-28j.
Note: the answer we got is a vector. Because momentum is a vector and therefore change in momentum is also a vector
To find the change in momentum of a particle under the force F=26i-12t2j from 1.0s to 2.0s, we first integrate the force over the given time interval. The change in the particle's momentum is found to be 26i - 20/3j kg*m/s.
The question involves calculating the change in momentum of a particle when a force F=26i-12t2j is applied from 1.0s to 2.0s. To find the change in momentum, we first need to integrate the force over the given time interval, because the change in momentum (Δp) is equal to the integral of the force over time, according to the impulse-momentum theorem, Δp = ∫t1t2 F dt.
For the i-component, the force is constant (26i), so its contribution to the change in momentum from 1.0s to 2.0s is simply 26i N multiplied by the time interval, which is 26i N * (2.0s - 1.0s) = 26i kg*m/s. For the j-component, the force varies with time (-12t2j), so we need to integrate this force from 1.0s to 2.0s. The integral of -12t2 from 1 to 2 gives us -∫12 12t2 dt = -[4t3/3]12 = -8 + 4/3 = -24/3 + 4/3 = -20/3. Thus, the change in momentum in the j-direction is -20/3 j kg*m/s.
Combining the i and j components, the total change in the particle's momentum between 1.0s and 2.0s is 26i - 20/3j kg*m/s.
8. Using a ramp 6 meters long, workers apply an effort force of 1250 N to move a
2000 N (F.) crate onto a platform 2 meters high. What is the efficiency of the
ramp? (Hint: calculate Win & Wout, then efficiency
The efficiency of the machine is 0.53 (53%).
Explanation:
The efficiency of a machine is given by:
[tex]\eta = \frac{W_{out}}{W_{in}}[/tex]
where
[tex]W_{out}[/tex] is the output work
[tex]W_{in}[/tex] is the work in input
The output work is:
[tex]W_{out}=F_L d_L = (2000)(2)=4000 J[/tex]
where
[tex]F_L = 2000 N[/tex] is the load
[tex]d_L = 2 m[/tex] is the distance covered by the load
The input work is:
[tex]W_{in}=F_E d_E = (1250)(6)=7500 J[/tex]
where
[tex]F_E = 1250 N[/tex] is the effort force
[tex]d_E = 6 m[/tex] is the distance from the effort to the pivot
Solving for the efficiency,
[tex]\eta=\frac{4000}{7500}=0.53[/tex]
So, the efficiency of the machine is 0.53 (53%).
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What height (displacement) will a ball reach if thrown upward with an initial velocity of 15 m/s
Answer:
11.48 m
Explanation:
initial velocity (u) = 15 m/s
acceleration due to gravity (g) = 9.8 m/s
final velocity (v) = 0 ( the ball's speed reduces gradually when thrown until
becomes 0 at maximum height)
find the height reached.
height (s) = ut + 0.5 at^{2}we cannot apply this formula directly because we do no know the time
(t), so we first need to find the time
v = u + at0 = 15 + (-9.8 x t) (the negative sign is because the ball is decelerating
upwards)
15 = 9.8t
t = 1.53 s
now that we have the time we can put it into the initial equationheight (s) = ut + 0.5 at^{2}height (s) = (15 x 1.53) + (0.5 x (-9.8) x 1.53^{2})
height = 22.95 - 11.47 = 11.48 m
an unbalanced force of 2 N ask on a 3 kg object for six seconds the magnitude of the objects change in velocity is
yes 1)18m/s 2)2m/s 3)36m/s 4)4.0m/s
The change in velocity is 4) 4.0 m/s
Explanation:
First of all, we can find the acceleration of the object, by applying Newton's second law:
[tex]F=ma[/tex]
where
F = 2 N is the net force on the object
m = 3 kg is the mass of the object
a is the acceleration
Solving for a,
[tex]a=\frac{F}{m}=\frac{2}{3}=0.67 m/s^2[/tex]
The motion of the object is a uniformly accelerated motion, so we can use the suvat equation:
[tex]v=u+at[/tex]
where
u is the initial velocity
v is the final velocity
[tex]a=0.67 m/s^2[/tex] is the acceleration
t = 6 s is the time elapsed
Therefore, the change in velocity is
[tex]v-u = at=(0.67)(6)=4.0 m/s[/tex]
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The angle between the two force of magnitude 20N and 15N is 60 degrees (20N force being horizontal) determine the resultant in magnitude and direction
A. If the force are pull
B. The 15N force is a push and 20N force is a pull
A) The resultant force is 30.4 N at [tex]25.3^{\circ}[/tex]
B) The resultant force is 18.7 N at [tex]43.9^{\circ}[/tex]
Explanation:
A)
In order to find the resultant of the two forces, we must resolve each force along the x- and y- direction, and then add the components along each direction to find the components of the resultant.
The two forces are:
[tex]F_1 = 20 N[/tex] at [tex]0^{\circ}[/tex] above x-axis
[tex]F_2 = 15 N[/tex] at [tex]60^{\circ}[/tex] above y-axis
Resolving each force:
[tex]F_{1x}=F_1 cos \theta = (20)(cos 0)=20 N\\F_{1y}=F_1 sin \theta =(20)(sin 0)=0 N[/tex]
[tex]F_{2x}=F_2 cos \theta = (15)(cos 60)=7.5 N\\F_{2y}=F_2 sin \theta =(15)(sin 60)=13.0 N[/tex]
So, the components of the resultant are:
[tex]F_x = F_{1x}+F_{2x}=20+7.5 = 27.5 N\\F_y = F_{1y}+F_{2y}=0+13.0=13.0 N[/tex]
And the magnitude of the resultant is:
[tex]F=\sqrt{F_x^2+F_y^2}=\sqrt{27.5^2+13.0^2}=30.4 N[/tex]
And the direction is:
[tex]\theta=tan^{-1}(\frac{F_y}{F_x})=tan^{-1}(\frac{13.0}{27.5})=25.3^{\circ}[/tex]
B)
In this case, the 15 N is applied in the opposite direction to the 20 N force. Therefore we need to re-calculate its components, keeping in mind that the angle of the 15 N force this time is
[tex]\theta=180^{\circ}-60^{\circ}=120^{\circ}[/tex]
So we have:
[tex]F_{2x}=F_2 cos \theta = (15)(cos 120)=-7.5 N\\F_{2y}=F_2 sin \theta =(15)(sin 120)=13.0 N[/tex]
So, the components of the resultant this time are:
[tex]F_x = F_{1x}+F_{2x}=20-7.5 = 12.5 N\\F_y = F_{1y}+F_{2y}=0+13.0=13.0 N[/tex]
And the magnitude is:
[tex]F=\sqrt{F_x^2+F_y^2}=\sqrt{13.5^2+13.0^2}=18.7 N[/tex]
And the direction is:
[tex]\theta=tan^{-1}(\frac{F_y}{F_x})=tan^{-1}(\frac{13.0}{13.5})=43.9^{\circ}[/tex]
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what is the mass of a cannonball whose velocity is 100 m/s if it were shot from a 2500 kg cannon that recoiled at a speed of 3 m/s
The mass of the cannonball is 75 kg
Explanation:
We can solve this problem by using the law of conservation of momentum: in fact, the total momentum of the ball-cannon system before and after the shot must be equal.
Before the shot, the total momentum is zero, since both objects are at rest:
[tex]p=0[/tex] (1)
After the shot, the total momentum is: given by:
[tex]p=mv+MV[/tex] (2)
where :
m kg is the mass of the cannonball
v = 100 m/s is the velocity of the ball
M = 2500 kg is the mass of the cannon
V = -3 m/s is the recoil velocity of the rifle (in the opposite direction to the ball
Since the toal momentum is conserved, (1) = (2), therefore we can solve for m, the mass of the cannonball:
[tex]0=mv+MV\\m=-\frac{MV}{v}=-\frac{(2500)(-3)}{100}=75 kg[/tex]
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Jessica stretches her arms out 0.8 m from the center of her body while holding a 2.0 kg mass in each hand. She then spins around on an ice rink at 1.2 m/s.
a. What is the combined angular momentum of the masses?
b. If she pulls her arms in to 0.12 m, what is her new linear speed?
Answer:
a) L = 3.84 kg m² / s, b) v = 0.96 m / s
Explanation:
a) the angular momentum is
L = I w
Linear and angular magnitudes are related
v = w r
w = v / r
The moment of inertia of a point mass is
I = m r²
We replace
L = 2 m r² v / r
The two is because they are two masses
L = 2 m r v
L = 2 2.0 0.8 1.2
L = 3.84 kg m² / s
b) The girl reduces the distance to 0.12 m
In this case the system is isolated, so the angular momentum is preserved
Initial moment,
L₀ = 3.84 kg m² / s
Final after shrugging arms
[tex]L_{f}[/tex] = I [tex]w_{f}[/tex]
L₀ = [tex]L_{f}[/tex]
3.84 = 2 2.0 0.12 wf
[tex]w_{f}[/tex] = 3.84 / 0.48
[tex]w_{f}[/tex] = 8 rad / s
Linear velocity is
v = w r
v = 8 0.12
v = 0.96 m / s
The combined angular momentum of the masses that Jessica is holding is 3.84 kg·m^2/s. After she pulls her arms in, her new linear speed is 3.84 m/s, calculated by the conservation of angular momentum, which states that L_initial = L_final.
Explanation:Calculating Angular Momentum and Linear Speed
To calculate the combined angular momentum of the masses that Jessica holds in her hands while spinning on the ice rink, we use the formula L = mvr, where L is the angular momentum, m is the mass, v is the linear velocity, and r is the radius or the distance from the center of her body to the mass.
Given:
m (mass) = 2.0 kg for each hand (two masses),
v (linear velocity) = 1.2 m/s,
r (radius) = 0.8 m.
The angular momentum for one mass is L = 2.0 kg × 1.2 m/s × 0.8 m. For both masses, we simply double this value:
L = 2(mvr) = 2(2.0 kg × 1.2 m/s × 0.8 m) = 3.84 kg · m^2/s.For part b, as Jessica pulls her arms in, her moment of inertia decreases and, according to the conservation of angular momentum, her linear speed must increase since angular momentum is conserved in the absence of external torques. The new radius r is now 0.12 m.
Let the new linear speed be v'. Using the conservation of angular momentum:
L_initial = L_finalmv_initialr_initial = mv'_finalr_finalv' = (mv_initialr_initial) / (mr_final)v' = (2.0 kg × 1.2 m/s × 0.8 m) / (2.0 kg × 0.12 m)v' = 3.84 m/s. So, the new linear speed is 3.84 m/s.Learn more about Angular Momentum here:https://brainly.com/question/37906446
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one feels diffulcites tobreath in a deep well while cleaning it, why?
Answer:
one feels diffulcites to breath in a deep well while cleaning it because well has less amount of oxygen in it.
A fired paper piece can be thrown to check the amount of oxygen.
Answer:
Because usually oxygen is on the ground, and then if you dig a hole, all kinds of gases scramble to run in, then oxygen is naturally less, which is also because of the depth of the ground. The deeper the ground, the more gas will press on you. Simply put, the deeper the well, the greater the pressure. Most of the carbon dioxide you emit in that well is held down by other gases and cannot go out, so that there is less oxygen.
A force of 350N is applied to a body. If the work done is 40kJ, what is the distance through which the body moved?
The distance covered by the body is 114.3 m
Explanation:
The work done by a force exerted on an object is given by
[tex]W=Fd cos \theta[/tex]
where
F is the magnitude of the force
d is the displacement of the object
[tex]\theta[/tex] is the angle between the direction of the force and of the displacement
For the object in this problem, we have
F = 350 N is the force applied
[tex]W=40 kJ = 40,000 J[/tex] is the work done
[tex]\theta=0^{\circ}[/tex] if we assume that the force is applied parallel to the motion of the object
Solving for d, we find the distance covered by the object:
[tex]d=\frac{W}{F cos \theta}=\frac{40,000}{(350)(cos 0)}=114.3 m[/tex]
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Place the items in order from the largest wavelength to the shortest wavelength.
Blue visible, Gamma radiation ,Green visible,Infrared, Microwave ,Orange visible ,Radio wave, Red visible, Ultraviolet (UV), Violet visible, X-ray ,Yellow visible
Brainliest???????? will i mark you???
From largest to shortest wavelength:
Radio waves, Microwaves, Infrared radiation, Red visible, Orange visible, Yellow visible, Green visible, Blue visible, Violet visible, Ultraviolet, X-rays, Gamma rays
Explanation:
Electromagnetic waves are oscillations of the electric and the magnetic field in a plane perpendicular to the direction of motion the wave.
Electromagnetic waves are the only type of waves able to travel in a vacuum, and in a vacuum they always at the same speed, the speed of light, equal to:
[tex]c=3.0\cdot 10^8 m/s[/tex]
Electromagnetic waves are classified into 7 different types, according to their wavelength/frequency. From slongest to shortest wavelength, they are ranked as follows:
Radio waves
Microwaves
Infrared radiation
Visible light
Ultraviolet
X-rays
Gamma rays
Visible light is the only part of the spectrum that the human eye is able to see. Depending on the wavelength of the visible light, we perceive the radiation as a different color. In order from longest to shortest wavelength, colors are:
Red
Orange
Yellow
Green
Blue
Indigo
Violet
Therefore, the correct order from largest to shortest wavelength in the given list is:
Radio waves
Microwaves
Infrared radiation
Red visible
Orange visible
Yellow visible
Green visible
Blue visible
Violet visible
Ultraviolet
X-rays
Gamma rays
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Answer:
From largest to shortest wavelength:
Radio waves, Microwaves, Infrared radiation, Red visible, Orange visible, Yellow visible, Green visible, Blue visible, Violet visible, Ultraviolet, X-rays, Gamma rays
Explanation:
Electromagnetic waves are oscillations of the electric and the magnetic field in a plane perpendicular to the direction of motion the wave.
Electromagnetic waves are the only type of waves able to travel in a vacuum, and in a vacuum they always at the same speed, the speed of light, equal to:
Electromagnetic waves are classified into 7 different types, according to their wavelength/frequency. From slongest to shortest wavelength, they are ranked as follows:
Radio waves
Microwaves
Infrared radiation
Visible light
Ultraviolet
X-rays
Gamma rays
Visible light is the only part of the spectrum that the human eye is able to see. Depending on the wavelength of the visible light, we perceive the radiation as a different color. In order from longest to shortest wavelength, colors are:
Red
Orange
Yellow
Green
Blue
Indigo
Violet
Therefore, the correct order from largest to shortest wavelength in the given list is:
Radio waves
Microwaves
Infrared radiation
Red visible
Orange visible
Yellow visible
Green visible
Blue visible
Violet visible
Ultraviolet
X-rays
Gamma rays
Explanation:
Suggest possible explanations why reaction times are different for different people?
Everyone has a different reaction time because not everyone reacts the same to situations. Some people may be faster or slower than others. It could be a result of age, health, and how they take care of themselves physically.
Gender, age, physical fitness, level of exhaustion, distraction, alcohol usage, personality type, the limb utilized for the test, biological rhythm, health, and whether the stimulus is auditory or visual have all been found to have an impact on reaction time. Social and cultural factors on reaction time are irrelevant.
What is reaction time?A reaction is a deliberate, free response to an outside stimulus. The reaction time is the amount of time between the administration of an external stimulus and the appropriate motor response.
The period between the introduction of the stimulus and the emergence of the subject's proper voluntary response is referred to as the reaction time.
Typically, it is measured in milliseconds. It depicts the rate at which stimuli operate on a person's sensory system to produce neurophysiological, cognitive, and informational processes.
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when a man travel from hilly region to terai region what will happen to his weight ? explain with reason.
Answer:
His weight increases.
Explanation:
The weight of the body is the gravitational force acting on the body at that location.The gravitational force is defined as the product of mass of the body and the acceleration due to gravity.W = m x g
The acceleration due to gravity of earth is high at the surface and decreases with respect to the height from the surface.Hence, a man in the higher altitude regions experience lower weight that in the the lower altitude regions.What acceleration will you give to a 24.3 kg box if you push it horizontally with a force of 85.5 N? Please show work.
The acceleration of a 24.3 kg box being pushed with a force of 85.5 N is approximately 3.52 m/s². This is determined through the application of Newton's Second Law (F=ma) where acceleration (a) is obtained when the applied force (F) is divided by the mass (m).
Explanation:The subject of the question is Physics, specifically the concept of Newton's Second Law. This law states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. It is represented by the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
In this case, we have the force F = 85.5 N and the mass m = 24.3 kg. You're asked to find out the acceleration, denoted by 'a'. You can find the acceleration by rearranging the formula to a = F/m. Substituting the given values into the formula gives a = 85.5 N / 24.3kg, resulting in an acceleration of approximately 3.52 m/s².
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the potential energy of an object decreases by 10J what is the change of the object's kenitic energy, assuming there is no friction in the system?
If the potential energy of an object decreases by 10J in a frictionless system, the kinetic energy increases by the same amount, 10J, due to the Law of Conservation of Energy.
Explanation:When the potential energy of an object decreases by 10J in a system with no friction, according to the Law of Conservation of Energy, there must be an equivalent increase in the object's kinetic energy. This is because the total mechanical energy (potential energy plus kinetic energy) of the system remains constant if no external work is done and no energy is lost to friction. Therefore, if the potential energy decreases by 10J, the kinetic energy will increase by 10J, assuming there is no energy lost to other forms like thermal energy or sound.
Final answer:
When potential energy decreases by 10J, the kinetic energy of the system increases by the same amount, following the Law of Conservation of Energy.
Explanation:
The potential energy of an object decreases by 10J, leading to a corresponding increase in kinetic energy by 10J. This change follows the Law of Conservation of Energy, where the loss of potential energy is accompanied by a gain in kinetic energy.
When there is no friction in the system, the energy transformation is purely between potential and kinetic energy, resulting in the described change. When potential energy decreases by 10J, the kinetic energy of the system increases by the same amount, following the Law of Conservation of Energy.
During study group Mary and Ben were arguing about a question on the practice test. The question said "True or False: The amount of mass of an object determines the amount of force that is needed to accelerate it." Mary said the answer was false, but Ben thinks it is true. Who is right? Justify your answer.
a.Mary is correct because according to Newton's first law it is unbalanced forces that cause an object to accelerate.
b. Ben is correct. According to Newton's 3rd law force is determined by mass.
c. Ben is correct. According to Newton's 2nd law of motion objects with more mass require more force to accelerate.
d. Mary is correct because it is the type of force that determines the acceleration, not the mass.
c. Ben is correct. According to Newton's 2nd law of motion objects with more mass require more force to accelerate.
Explanation:
We can answer this question by using Newton's second law of motion, which states that the net force applied on an object is equal to the product between the mass of the object and its acceleration. Mathematically:
[tex]F=ma[/tex]
where
F is the net force
m is the mass of the object
a is its acceleration
From the equation, we notice that:
- The force is directly proportional to the mass of the object --> so if the mass increases, the force needed to accelerate the object will increase too
Therefore, the correct answer is
c. Ben is correct. According to Newton's 2nd law of motion objects with more mass require more force to accelerate.
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help asap!!! Describe the distinction between speed and velocity. Be sure to include
examples of each.
The distinctions between speed and the velocity is as follows:
Speed:
“Speed” is a “scalar quantity”. “Speed” of the “vehicle” says that “rate of the distance traveled” by “the vehicle”. For example, consider that a car is moving with “the speed 5 Km/h”. It informs that the “car can move 5 Km in one hour”.Velocity:
“Velocity” is a “vector quantity”. “Velocity” of the “vehicle” says that “rate of the distance traveled” and “the direction of the vehicle”. For example, consider a car is moving with “5 km/h west”. It informs that car is traveling in “direction of west” it covers “5 Km in one hour”.Which statement best describes how reproduction leads to natural selection in a population?
Organisms do not produce many offspring, so all of them can survive and pass on their traits.
Organisms overproduce offspring; consequently, all of them are likely to survive and pass on traits.
Organisms overproduce offspring, so only some survive and pass on their traits.
Organisms do not overproduce offspring; therefore, those that are produced will develop the best traits.
Organisms overproduce offspring, so only some survive and pass on their traits.
Natural selection is the fitting of a population to its environment.
Explanation:
Most organisms produce more than two or more offspring in their lifetime. Therefore the subsequent generations ideally have more individuals than the previous. However, naturally, the population size does not grow indefinitely. This is because some individuals do not survive to pass their genes to the next generation. Natural selection chooses the best fit individuals to habitat, and these live long enough to pass their traits to the next generation. Natural selection powers the evolution of a population even as environment changes
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Answer:
The answer is C) Organisms overproduce offspring, so only some survive and pass on their traits
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What are some sir issac newtons greatest accomplishments?
Answer:#1 NEWTON’S THREE LAWS OF MOTION LAID THE FOUNDATION OF CLASSICAL MECHANICS #2 HE WAS THE FIRST TO FORMULATE THE NOTION OF GRAVITY AS A UNIVERSAL FORCE
#3 NEWTON’S PRINCIPIA IS ONE OF THE MOST IMPORTANT WORKS IN THE HISTORY OF SCIENCE
#4 HE DISCOVERED THE GENERALISED BINOMIAL THEOREM IN 1665
#5 ISAAC NEWTON INVENTED CALCULUS
#6 HE INVENTED THE FIRST REFLECTING TELESCOPE
#7 HE DID GROUND BREAKING WORK IN OPTICS
#8 HE IDENTIFIED LIGHT AS THE SOURCE OF COLOUR SENSATION
#9 HE INFERRED CORRECTLY THE OBLATENESS OF EARTH’S SPHEROIDAL FIGURE
#10 SIR ISAAC NEWTON WAS THE SECOND SCIENTIST TO BE KNIGHTED
Answer:
Invented the reflecting telescope.
Proposed new theory of light and color.
Discovered calculus.
Developed three laws of motion.
Devised law of universal gravitation.
Advanced early modern chemistry.
Explanation:
Sir Isaac Newton had many great accomplishments. Here are some of his most notable achievements:
1. Newton's Three Laws of Motion: Newton formulated three fundamental laws that laid the foundation of classical mechanics. These laws describe how objects move and interact with each other. They are still widely used today to understand and predict the motion of objects.
2. Formulation of Gravity: Newton was the first to formulate the notion of gravity as a universal force. He explained that every object with mass attracts other objects towards it. His understanding of gravity helped explain why objects fall to the ground and why planets orbit the Sun.
3. Principia: Newton's book called "Mathematical Principles of Natural Philosophy" (commonly known as "Principia") is one of the most important works in the history of science. In this book, Newton presented his laws of motion and the law of universal gravitation. It revolutionized the field of physics and became the foundation for classical mechanics.
4. Generalized Binomial Theorem: In 1665, Newton discovered the generalized binomial theorem, which is a mathematical formula used to expand powers of binomials (expressions with two terms). This theorem is still studied and applied in various branches of mathematics.
5. Invention of Calculus: Newton independently developed calculus, a branch of mathematics that deals with rates of change and the accumulation of quantities. Calculus is widely used in many fields, including physics and engineering, and it provides a powerful tool for solving problems involving change and motion.
6. Invention of the Reflecting Telescope: Newton constructed the first reflecting telescope, which used mirrors instead of lenses to gather and focus light. This invention greatly improved the quality and clarity of images observed through telescopes and had a significant impact on the field of astronomy.
7. Groundbreaking Work in Optics: Newton conducted groundbreaking experiments and made important discoveries in the field of optics. He demonstrated that white light is composed of different colors, which led to the understanding of the color spectrum. His work on optics laid the foundation for future developments in this field.
8. Identification of Light as the Source of Color Sensation: Newton proposed that light is the source of color sensation. He demonstrated that the colors we perceive are a result of how light interacts with objects and our eyes. This understanding of light and color perception has had lasting effects in fields like art and design.
9. Inference of Earth's Oblateness: Newton correctly inferred that the Earth is not a perfect sphere but rather oblate, meaning it is slightly flattened at the poles and bulges at the equator. His understanding of the Earth's shape was based on his knowledge of gravity and the forces acting on the planet.
10. Knighthood: Newton was knighted by Queen Anne in 1705, becoming the second scientist to receive this honor. His contributions to science and mathematics were recognized and celebrated during his lifetime.
Which factors affect heat transfer between a warm and a cool substance?
the time it took to hear the substance, the area of contact and the specific heats of the substances
the amount of time of contact, the area of contact, and the specific heals of the substances
the time it took to heat the substance, the area of the substances, and the specific heats of the substances
the amount of time of contact, the area of the substances, and the specific heats of the substances
The heat transfer depends on the factors such as the amount of time of contact, the area of contact, and the specific heals of the substances.
What is Heat Transfer?The process of flow of energy from a body of higher temperature to a lower temperature is known as heat transfer.
The mathematical expressions governing the concept of heat transfer are given as follows-
Q = m × c × ΔT
here,
m is the mass of the body.
c is the specific heat.
ΔT is the change in temperature.
And,
Q = k × A×ΔT / L
here,
k is the thermal conductivity.
A is the area of contact and L is the length of the body.
So, clearly, heat transfer depends on the factors such as specific heat and the area of contact. Moreover, the time of contact is also a matter of discussion as the longer the contact time, the more amount of energy will get a transfer from one body to another.
Thus, we can conclude that the heat transfer depends on the factors such as the amount of time of contact, the area of contact, and the specific heals of the substances.
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how do i work out these?
Answer:
2. 0.27 N/kg
3a. 210 N
3b. 23.3 N
Explanation:
The acceleration due to gravity is:
g = GM / r²
where G is the gravitational constant, M is the mass of the planet, and r is the distance from the planet's center.
2. At the surface of the Earth (r = R), the acceleration due to gravity is 9.8 N/kg.
9.8 = GM / R²
At r = 6R, the acceleration due to gravity is:
g = GM / (6R)²
g = (GM / R²) / 36
g = 9.8 / 36
g = 0.27 N/kg
3a. Weight is mass times acceleration due to gravity:
W = mg
W = (20 kg) (10.5 N/kg)
W = 210 N
3b. Find the new value of g:
g = GM / (3R)²
g = (GM / R²) / 9
g = 10.5 / 9
g = 1.17 N/kg
Now find the weight:
W = mg
W = (20 kg) (1.17 N/kg)
W = 23.3 N
A person absentmindedly walks off the edge of a tall cliff. They will fall 50 m into either
deadly rocks or a safe lake below the cliff. The lake is 12 meters away from the edge of
the cliff
If the person walks off the cliff at a constant velocity of 3.8 m/s,
will they survive? No (yes or no) How far did they go?
The man lands 12.1 m far from the base of the cliff, so he will survive
Explanation:
The motion of the person is a projectile motion, which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction
We start by considering the vertical motion, to find the time of flight of the person, with the following suvat equation:
[tex]s=ut+\frac{1}{2}gt^2[/tex]
where :
s = 50 m is the vertical displacement of the man (the height of the cliff)
t is the time of flight
u = 0 is the initial vertical velocity
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Solving for t, we find
[tex]t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(50)}{9.8}}=3.19 s[/tex]
Now we know that the man moves horizontally, with a constant velocity of
[tex]v_x = 3.8 m/s[/tex]
Therefore, the horizontal distance covered by the man during this time is
[tex]d=v_x t = (3.8)(3.19)=12.1 m[/tex]
So the man lands 12.1 m far from the base of the cliff: therefore, on the lake, so he will survive.
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What scientific question does Isaac Asimov most clearly address with his
story "Runaround"?
A. Should robots be allowed to marry?
B, should robots be treated as members of the family?
C. Can robots be trained to follow a moral code?
D.
Can robots be trained to be the sole caretakers of children?
Answer: C. can robots be trained to follow a moral code?
Explanation:
Answer:
Its C
Explanation:
An analogy makes a comparison between objects based on their similar qualities. Cassidy wanted to create an analogy for the motion of atoms in solids, liquids, and gases, so she compared them to marbles in a tray. Which best compares the phases of matter to marbles in a tray?A) A solid is like the tray being shaken and the marbles moving around it, and a liquid is like the tray being shaken slowly and all the marbles moving in their positions.B) A solid is like the tray being shaken slowly and all the marbles moving in their positions, a liquid is like the tray being shaken and the marbles moving around it, and a gas is like the tray being shaken hard and the marbles moving vigorously around it.C) A gas is like the tray being shaken slowly and all the marbles moving in their positions, and a solid is like the tray being shaken hard and the marbles moving vigorously around it.D) A liquid is like the tray being shaken hard and the marbles moving vigorously around it, and a gas is like the tray being shaken slowly and all the marbles moving in their positions.
Answer:
A solid is like the tray being shaken slowly and all the marbles moving in their positions, a liquid is like the tray being shaken and the marbles moving around it, and a gas is like the tray being shaken hard and the marbles moving vigorously around it
Explanation:
its b
A solid is like the tray shaken slowly and all the marbles will move in their positions. A liquid is like the tray being shaken and the marbles will move around it. A gas is like the tray being shaken hard and the marbles will move vigorously around it. Therefore, option (B) is correct.
What are states of matter?The matter exists in various forms in nature. Some substances have a definite shape such as wood, stone, marbles and some can flow, take the any shape such as water, while there are forms of matter that do not have definite shapes.
In solids, the molecules are very tightly packed and thus solids have a definite and rigid structure. The compact packing of solids indicates that the molecules are too close to each other and the molecules do not show any movement. The kinetic energy of molecules or atoms in the solid is the least or negligible.
In liquids, the molecules are at some distance from each other and they show some movements. Since the molecules show significant movement, so they have significant amount of kinetic energy. The kinetic energy of molecules or atoms in the liquid is more than that of solids.
In gases, the molecules or atoms are farther from each other and thus their molecules show huge movement. The kinetic energy of molecules or atoms in gases is the greatest in comparison to solids and liquids.
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Which choice can be defined as the space around any charged particle that is directed away from a positive charge and towards a negative charge?
gravitational field
magnetic field
proton field
electric field
Answer:electric field
Explanation:Because in an electric field, positive charge is directed away and negative charge is directed towards the electric field.
Answer:
an electric field
Explanation:
this field is what is direted to a negative charge
how much electrical energy is used by a 400 W toaster that is operating for 5 minutes?
The electrical energy consumed by a toaster is 0.033 Kwh.
Explanation:
The power utilized by the toaster is 400 W.
[tex]\text { The power utilized by the toaster is } 400 \mathrm{W} \text { in kilo-watts is } \frac{400}{1000}=0.4 \mathrm{Kw}[/tex]
The toaster is operated for 5 Minutes.
[tex]\text { The toaster is operated for } 5 \text { Minutes in hours is } \frac{5}{60}=0.083 \text { hours. (One minute is } 60 \text { seconds) }[/tex]
We know that,
[tex]\text {power}=\frac{\text {energy}}{\text {time}}[/tex]
Substitute the values in the above formula to obtain electrical energy,
[tex]0.4=\frac{\text { energy }}{0.083}[/tex]
Electrical energy = 0.4 × 0.083
Electrical energy is 0.033 Kwh.
Answer:
The answer is 120,000 Joules
Explanation:
Someone throws their laptop with a horizontal component of velocity of 25 m/s. It takes the laptop 3.00 seconds to come back to the original height. Calculate the horizontal range and the initial vertical component of velocity
1) The horizontal range of the laptop is 75.0 m
2) The initial vertical component of the velocity is 14.7 m/s
Explanation:
1)
The motion of the laptopin this problem is a projectile motion, so it follows a parabolic path which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- An accelerated motion with constant acceleration (acceleration of gravity) in the vertical direction
To find the horizontal range of the laptop, we just need to analyze its horizontal motion.
We know that:
- The laptop moves horizontally with a constant velocity of [tex]v_x = 25 m/s[/tex]
- The time of flight of the laptop is [tex]t=3.00 s[/tex]
So, the horizontal range of the laptop is given by
[tex]d=v_x t = (25)(3.00)=75.0 m[/tex]
2)
The total time of flight of a projectile is given by
[tex]t=\frac{2u_y}{g}[/tex]
where
[tex]u_y[/tex] is the initial vertical component of hte velocity
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Here we know that the time of flight is
[tex]t=3.00 s[/tex]
Therefore, we can solve the formula for [tex]u_y[/tex], to find the initial vertical velocity:
[tex]u_y = \frac{tg}{2}=\frac{(3.00)(9.8)}{2}=14.7 m/s[/tex]
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If Mary is 3m from her reflection, how far is mary from the mirror?
Final answer:
Mary is 1.5m from the mirror, as the distance to her reflection, which is 3m, includes the distance to the mirror and the equal distance from the mirror to the reflection.
Explanation:
If Mary is 3m from her reflection in a mirror, it implies that she is 1.5m from the mirror itself. This is because the law of reflection states that the distance from the object to the mirror is equal to the distance from the mirror to the image of that object. Therefore, in this case, the 3m distance is double the actual distance between Mary and the mirror since it includes the path to the mirror and the equal path from the mirror to the image.
a 50 kg pole vaulter drops vertically from a height of 4 meters coming to rest just .4s after his feet touch the ground, what is his momentum just before his feet touch the ground? what net force acts on him during his acceleration?
1) His momentum before touching the ground is 442.5 kg m/s
2) The net force on the pole vaulter is 490 N
Explanation:
1)
The motion of the pole vaulter is a motion of free fall, so it is subjected only to the force of gravity. Therefore, he falls to the ground at constant acceleration ([tex]g=9.8 m/s^2[/tex], acceleration of gravity), so we can use the following suvat equation to find his final velocity:
[tex]v^2-u^2=2as[/tex]
where
v is the final velocity
u = 0 is the initial velocity
[tex]a=g[/tex] is the acceleration
s = 4 m is the distance covered during the fall
Solving for v,
[tex]v=\sqrt{u^2+2as}=\sqrt{0+2(9.8)(4)}=8.85 m/s[/tex]
And therefore, his final momentum before touching the ground is
[tex]p=mv[/tex]
where m = 50 kg is his mass. Substituting,
[tex]p=(50)(8.85)=442.5 kg m/s[/tex]
2)
As we said previously, the only force acting on the pole vaulter during his fall is the force of gravity, which is
[tex]F=mg[/tex]
where
m = 50 kg is the mass
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Substituting, we find the force of gravity, and therefore the net force acting on the pole vaulter:
[tex]F=(50)(9.8)=490 N[/tex]
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What is the definition of a neutron?
Answer:
neutron is a subatomic particle of about the same mass as a proton but without an electric charge, present in all atomic nuclei except those of ordinary hydrogen.
Answer:
According to Oxford dictionary neutron is a subatomic particle of about the same mass as a proton but without an electric charge, present in all atomic nuclei except those of ordinary hydrogen.
A 55 kg person is sitting in a car that hits a concrete floor.The car was moving at 30 m/s and came to a halt in 0.35s.What is the average force that the seatbelt exerts on the person.
Answer:
-4714.28N
Explanation:
Given
Mass of person, m= 55 kgCar speed initially ,u =30[tex]\frac{m}{sec}[/tex]Car speed finally, v=0(car comes to a halt)Duration for the car to come halt,t=0.35 secThis question is based on the concept of Impulse
Impulse is the force acting in a time interval(usually very short)
it is equal to force multiplied with time and also equal to change in momentum of body
⇒[tex]F\times t= mv-mu\\F \times0.35= 55\times (0-30)\\F\times 0.35= -1650\\F= -4714.28 N[/tex]
Therefore the seat belt exerts a force of -4718.28N on the person
The negative sign signifies that seat belt exerts force in opposite direction of Force
The average force exerted by the seatbelt on a 55 kg person in a car that decelerates from 30 m/s to a halt in 0.35s is 4714.05 N, acting in the direction opposite to the motion.
To calculate the average force that the seatbelt exerts on a person, we can use the formula derived from Newton's Second Law of Motion:
F = ma
However, since acceleration is not directly given, we can find it using the formula for acceleration (a) in terms of velocity change (∆v) and time (∆t):
a = ∆v / ∆t
In this case:
The velocity change (∆v) is 30 m/s (since the car stops, the final velocity is 0 and initial velocity is 30 m/s).The time (∆t) over which the velocity change occurs is 0.35s.Now, we will calculate the acceleration experienced by the person:
a = -30 m/s / 0.35s = -85.71 m/s² (The negative sign indicates deceleration).
Using the calculated acceleration and the person's mass (55 kg), we can find the force:
F = 55 kg imes -85.71 m/s² = -4714.05 N
The negative sign indicates the direction of the force is opposite to the direction of motion. The average force exerted by the seatbelt on the person is therefore 4714.05 N.