The amplitude is 0.077 m
Explanation:
The period of a spring-mass system is given by
[tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]
where
m is the mass
k is the spring constant
For the system in this problem, we have
m = 304 g = 0.304 kg is the mass
T = 0.467 s is the period
Solving for k, we find the spring constant:
[tex]k=(\frac{2\pi}{T})^2 m=(\frac{2\pi}{0.467})^2(0.304)=55.0 N/m[/tex]
The total energy of an oscillating system is given by
[tex]E=\frac{1}{2}kA^2[/tex]
where A is the amplitude of the oscillation. In this problem, we know that
k = 55.0 N/m
E = 0.163 J is the total energy
Solving for A, we find the amplitude:
[tex]A=\sqrt{\frac{2E}{k}}=\sqrt{\frac{2(0.163)}{55.0}}=0.077 m[/tex]
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A snowmobile is used to pull one sled across the ice. The mass of the snowmobile and the rider is 315 kg. The mass of the sled is 150 kg. The coefficient of kinetic friction for the sled on ice is 0.15 and the coefficient of kinetic friction on the snowmobile is 0.25. The acceleration of the snowmobile and the sled is 1.9/s^2.
a. What is the net force acting on the system?
b. What is the tension in the rope between the sled and the snowmobile?
c. What is the applied force on the snowmobile?
a) The net force on the system is 883.5 N
b) The tension in the rope is 505.5 N
c) The applied force is 1875.8 N
Explanation:
a)
We start by considering the whole system snowmobile+sled. We can apply Newton's second law:
[tex]\sum F = (m+M)a[/tex]
where
[tex]\sum F[/tex] is the net force on the system
m = 150 kg is the mass of the sled
M = 315 kg is the mass of the snowmobile+rider
[tex]a=1.9 m/s^2[/tex] is the acceleration
Substiting the values into the equation, we find the net force:
[tex]\sum F=(150+315)(1.9)=883.5 N[/tex]
b)
Now we consider only the forces acting on the sled. Again, we apply Newton's second law:
[tex]T-F_f = ma[/tex]
where:
T is the tension in the rope, which pulls the sled forward
[tex]F_f[/tex] is the frictional force acting on the sled, which acts backward
m = 150 kg is the mass of the sled
[tex]a=1.9 m/s^2[/tex] is the acceleration
The force of friction on the sled is given by
[tex]F_f = \mu mg[/tex]
where
[tex]\mu=0.15[/tex] is the coefficient of friction of the sled on ice
m = 150 kg
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Substituting and solving for T, we find:
[tex]T-\mu mg = ma\\T=m(a+\mu g)=(150)(1.9+0.15 \cdot 9.8)=505.5 N[/tex]
c)
Now we consider instead the forces acting on the snowmobile+rider only. Applying again Newton's second law,
[tex]F-F_F-T = Ma[/tex]
where
F is the applied force, which pushes the snowmobile forward
[tex]F_F[/tex] is the force of friction acting backward on the snowmobile
T = 505.5 N is the tension in the rope, which pulls the snowmobile backward
M = 315 kg is the mass of the snowmobile+rider
[tex]a=1.9 m/s^2[/tex] is the acceleration
The force of friction on the snowmobile is given by
[tex]F_F = \mu Mg[/tex]
where
[tex]\mu=0.25[/tex] is the coefficient of friction of the snowmobile on ice
m = 315 kg
[tex]g=9.8 m/s^2[/tex]
Substituting and solving for F, we find the applied force:
[tex]F=Ma+\mu Mg+T=(315)(1.9)+(0.25)(315)(9.8)+505.5=1875.8 N[/tex]
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Consider this situation: A child is holding onto a tree rope and swinging through the air.
Of the forces listed, identify which act upon the child.
a. Normal Force
b. Gravity Force
c. Applied Force
d. Friction Force
e. Tension Force
f. Air Resistance Force
Final answer:
In the scenario of a child swinging on a rope, the acting forces are the gravity force, tension force, and air resistance force. Normal force and applied force are not directly acting on the child in the swing, and friction force is not a significant factor in this context.
Explanation:
When a child is swinging through the air while holding onto a tree rope, the child is subject to several forces. Among the forces listed, the following forces act upon the child:
Gravity Force: This is also known as weight, represented by W in the free-body diagram. It pulls the child directly downwards towards the center of the Earth.
Tension Force: Represented by T in the free-body diagram, this force is exerted by the rope on the child, pulling upwards and often inclined depending on the motion of the swing.
Air Resistance Force: As the child swings, they encounter air resistance that opposes their motion through the air.
The normal force does not act upon the child while they are swinging because there is no perpendicular contact with a solid surface like the ground or a table. Applied force would be present if someone or something else is pushing the child to start the swinging motion or to keep it going. However, for the child simply swinging, we do not consider an ongoing applied force. Friction force is usually associated with contact between two surfaces, such as the wheels of a wagon rolling on the ground. Therefore, friction is not a significant factor when considering a child swinging on a rope.
Using this understanding, we can create a free-body diagram that includes only external forces such as gravity force, tension force, and air resistance force to analyze the child's motion.
a cube of mass 128g has density of 2g/^3 what is the length each side of cube
The length of the side of the cube is 4 cm
Explanation:
The density of the cube is given by:
[tex]\rho=\frac{m}{V}[/tex]
where
m is the mass of the cube
V is its volume
Also, the volume of the cube is given by
[tex]V=L^3[/tex] (2)
where L is the length of each side.
For the cube in this problem we have:
m = 128 g
[tex]\rho=2 g/cm^3[/tex]
From the first equation, we find the volume of the cube:
[tex]V=\frac{m}{\rho}=\frac{128}{2}=64 cm^3[/tex]
And now we use eq.(2) to find the length of the side:
[tex]L=\sqrt[3]{V}=\sqrt[3]{64}=4 cm[/tex]
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The length of each side of a cube with a mass of 128 grams and a density of 2 grams per cubic centimeter is 4 centimeters.
To find the length of each side of a cube with a mass of 128 grams and a density of 2 grams per cubic centimeter, we can use the formula for density which is mass divided by volume. Since density is given in grams per cubic centimeter (g/cm3), we'll keep the mass in grams and calculate the volume in cubic centimeters. First, we calculate the volume of the cube by dividing the mass by the density (Volume = Mass / Density).
Volume = 128g / 2g/cm3 = 64 cm3
Because the volume of a cube is also the cubic of the length of its side (Volume = side3), we can now find the length of one side by taking the cube root of the volume.
Length of one side = \3\sqrt{64 cm3} = 4 cm
Therefore, each side of the cube is 4 centimeters in length.
A box is pushed 40 m by a mover. The amount of work done was 2,240 j. How much force was exerted on the box
The force exerted on the box is 56 N
Explanation:
The work done by a force 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 box in this problem, we have:
W = 2240 J is the work done
d = 40 m is the displacement of the box
Assuming that the force is parallel to the displacement, [tex]\theta=0[/tex]
Solving the equation for F, we find the force exerted on the box:
[tex]F=\frac{W}{d cos \theta}=\frac{2240}{(40)(cos 0)}=56 N[/tex]
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This is a __________ reaction and the product(s) is/are
A) single replacement; zinc chloride and hydrogen gas.
B) double replacement; zinc oxide and hydrogen gas.
C) synthesis; zinc chloride and hydrogen gas.
D) decomposition; zinc chloride and water.
Answer: This is a single displacement reaction and the products are zinc chloride and hydrogen gas.
Explanation:
Single displacement reaction is defined as the reaction in which more reactive element displaces a less reactive element from its chemical reaction.
[tex]AB+C\rightarrow CB+A[/tex]
Element C is more reactive than element A.
Double displacement reaction is defined as the reaction in which exchange of ions takes place.
[tex]AB+CD\rightarrow CB+AD[/tex]
Synthesis reaction is defined as the reaction in which smaller substances combine in their elemental state to form a larger substance.
[tex]A+B\rightarrow AB[/tex]
Decomposition reaction is defined as the reaction in which a large substance breaks down into smaller substances.
[tex]AB\rightarrow A+B[/tex]
For the given chemical reaction:
[tex]Zn(s)+2HCl(aq.)\rightarrow ZnCl_2(aq.)+H_2(g)[/tex]
The reaction is considered as single displacement reaction.
By Stoichiometry of the reaction:
1 mole of zinc metal reacts with 2 moles of hydrochloric acid to produce 1 mole of zinc chloride and 1 mole of hydrogen gas.
Hence, this is a single displacement reaction and the products are zinc chloride and hydrogen gas.
When the 3.0 kg cylinder fell 500 m, the final temperature of the water was °C and the change in temperature was °C.
When the 9.0 kg cylinder fell 500 m, the final temperature of the water was °C and the change in temperature was °C.
Answer:
A.28.52
B.3.52
C.35.55
D.10.55
just guessed and got it right lol
Answer:
A.28.52, B.3.52, C.35.55, D.10.55
Explanation:
the draw plant pluto has a mass of 1.30 x10 to the 22 power kg and a radius of 1,188km what is the acceleration of gravity(g) on the surface of Pluto?
The acceleration of gravity on the surface of Pluto is [tex]0.61 m/s^2[/tex]
Explanation:
The acceleration of gravity at the surface of a planet is given by the equation:
[tex]g=\frac{GM}{R^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
M is the mass of the planet
R is the radius of the planet
For Pluto, we have:
[tex]M=1.30\cdot 10^{22} kg[/tex] is the mass
[tex]R=1,188 km = 1.188\cdot 10^6 m[/tex] is the radius
Substituting, we find its gravitational acceleration:
[tex]g=\frac{(6.67\cdot 10^{-11})(1.30\cdot 10^{22})}{(1.188\cdot 10^6)^2}=0.61 m/s^2[/tex]
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12345678910
As a sound wave travels from liquid water into ice, its wavelength would
Stretch.
Hope this helps.
A piece of magnetic material that retains its magnetic properties after it is removed from a magnetic field.
Answer: d
Explanation: Unscrew one light, if the others remain on it is a parallel circuit.
A 4 kg textbook sits on a desk. It is pushed horizontally with a 50 N applied force against a 15 N frictional force.
a. Draw a free body diagram for the textbook.
b. What is the motion in the vertical?
c. What is the net horizontal force acting on the book?
d. What is the net force acting on the book?
e. What is the acceleration of the book?
Answer:
a. See attached diagram
b. There is no vertical motion
c. Net horizontal force: 35 N
d. Total net force: 35 N
e. Acceleration of the book: 8.75 m/s^2
Explanation:
Please see attached diagram for all the forces acting on the book:
Forces acting vertically:
1) The book's weight (force exerted by gravity) is pictured in purple pointing down and labeled "w".
2) The normal force the table exerts on the book as reaction, is pictured in blue pointing up, and labeled "n". It cancels with the force of gravity, so there is no vertical movement since gravitational force and the normal are the only forces acting in the vertical direction.
Forces acting horizontally:
1) the pushing 50 N force is pictured in green and pointing to the right, parallel to the surface of the table.
2) the 15 N force of friction is pictured in red, and acting in opposite direction to the pushing force. It is represented by a shorter vector than the pushing force due to the fact that its magnitude is smaller.
In this horizontal direction there is a net force that is propelling the object in horizontal motion. This net force is the difference between the 50 N force and the 15 N force, resulting in a 35 N force pointing in the same direction as the pushing force.
The net horizontal force is 35 N in magnitude.
The addition of all forces acting is dominated by the horizontal components, since the vertical acting forces cancel each other. Therefore, the total net force acting on the book is the 35 N resulting horizontal force.
The acceleration of the book can be calculated via Newton's second law of motion:
[tex]F_{net}=m\,*\,a\\35 N = 4\,kg\,*a\\a=\frac{35}{4} \,\frac{m}{s^2} \\a=8.75\, \frac{m}{s^2}[/tex]
Which sequence of moon phases is correct? .
new moon, waxing crescent, full moon, waning gibbous
first quarter, new moon, full moon, third quarter
waning crescent, full moon, waxing crescent, new moon
full moon, waxing crescent, waning crescent, new moon
Answer:
d
Explanation:
this is the order of the moons ( you can look it up too)
The correct sequence of moon phases is: new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third quarter, waning crescent. The cycle follows the moon as it appears illuminated from Earth.
Explanation:The correct sequence of the moon phases is: new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third quarter, and waning crescent. The cycle starts with the new moon when the moon is not visible from Earth. The moon then enters the waxing crescent phase when a thin sliver of the moon becomes visible. The first quarter is when half of the moon is illuminated. This is followed by the waxing gibbous phase when more than half but not fully illuminated. The full moon phase is when the entire face of the moon is illuminated. The moon then begins to wane and less of it is illuminated each night. Waning gibbous phase comes first, followed by the third quarter phase when half of the moon is illuminated. The cycle ends with the waning crescent phase when again only a sliver of the moon is visible before transitioning back to a new moon.
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We all know that in the earth gravity is there,but why clouds doesn't fall down???
Answer: Clouds are evaporated sea water. You should be asking "Why does the gravity on Earth pull us down and not evaporated water.
Explanation:
Answer:
Because of their mass
Explanation:
Clouds are made of water right ? so you are asking why they don't fall down if air is lighter than water .
The two biggest reasons the clouds stay in the sky are
1. Small Drops
2. Wind
Small drops of water fall more slowly than big drops, as the drops of the clouds fall thought the air, the air pushes back to them, because Small drops has less mass than large drops, clouds can only contain small drops of water.
A block is at rest on the incline shown in the figure. The coefficients of static and ki- netic friction are μs = 0.62 and μk = 0.53, respectively.
2
29◦
What is the frictional force acting on the 46 kg mass?
The frictional force is 218.6 N
Explanation:
The block in the problem is at rest along the inclined surface: this means that the net force acting along the direction parallel to the incline must be zero.
There are two forces acting along this direction:
- The component of the weight parallel to the incline, downward along the plane, of magnitude
[tex]mg sin \theta[/tex]
where
m = 46 kg is the mass
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]\theta=29^{\circ}[/tex] is the angle of the incline
- The (static) frictional force, acting upward, of magnitude [tex]F_f[/tex]
Since the block is in equilibrium, we can write
[tex]mg sin \theta - F_f = 0[/tex]
And substituting, we find the force of friction:
[tex]F_f = mg sin \theta = (46)(9.8)(sin 29^{\circ})=218.6 N[/tex]
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4. A safe is hurled down from the top of a 1.3 x 102 m
building at a speed of 11.0 m/s. What is its velocity as
it hits the ground?
The final speed of the safe is 51.7 m/s
Explanation:
The motion of the safe is a free fall motion, which is a motion at constant acceleration ([tex]g=9.8 m/s^2[/tex], towards the ground). Therefore, we can apply the following suvat equation:
[tex]v^2-u^2=2as[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the displacement
In this problem we have (taking downward as positive direction):
u = 11.0 m/s
[tex]a=g=9.8 m/s^2[/tex]
[tex]s=1.3\cdot 10^2 m= 130 m[/tex] is the vertical displacement (the height of the building)
Solving for v, we find the final velocity (and so, the final speed):
[tex]v=\sqrt{u^2+2as}=\sqrt{11.0^2+2(9.8)(130)}=51.7 m/s[/tex]
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- 4x4 – 13x3 + 8x2 – 21x + 18 is divided by 2 – 3?
Answer:
x = 3/4 or x = ((-1)^(1/3) (127 - 18 sqrt(43))^(2/3) - 13 (-1)^(2/3))/(3 (127 - 18 sqrt(43))^(1/3)) - 4/3 or x = 1/3 (13 (-1/(127 - 18 sqrt(43)))^(1/3) - (-1)^(1/3) (18 sqrt(43) - 127)^(1/3)) - 4/3 or x = (-(127 - 18 sqrt(43))^(2/3) - 13)/(3 (127 - 18 sqrt(43))^(1/3)) - 4/3
Explanation:
Solve for x over the real numbers:
4 x^4 + 13 x^3 - 8 x^2 + 21 x - 18 = 0
The left hand side factors into a product with two terms:
(4 x - 3) (x^3 + 4 x^2 + x + 6) = 0
Split into two equations:
4 x - 3 = 0 or x^3 + 4 x^2 + x + 6 = 0
Add 3 to both sides:
4 x = 3 or x^3 + 4 x^2 + x + 6 = 0
Divide both sides by 4:
x = 3/4 or x^3 + 4 x^2 + x + 6 = 0
Eliminate the quadratic term by substituting y = x + 4/3:
x = 3/4 or 14/3 + 4 (y - 4/3)^2 + (y - 4/3)^3 + y = 0
Expand out terms of the left hand side:
x = 3/4 or y^3 - (13 y)/3 + 254/27 = 0
Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:
x = 3/4 or 254/27 - 13/3 (z + λ/z) + (z + λ/z)^3 = 0
Multiply both sides by z^3 and collect in terms of z:
x = 3/4 or z^6 + z^4 (3 λ - 13/3) + (254 z^3)/27 + z^2 (3 λ^2 - (13 λ)/3) + λ^3 = 0
Substitute λ = 13/9 and then u = z^3, yielding a quadratic equation in the variable u:
x = 3/4 or u^2 + (254 u)/27 + 2197/729 = 0
Find the positive solution to the quadratic equation:
x = 3/4 or u = 1/27 (18 sqrt(43) - 127)
Substitute back for u = z^3:
x = 3/4 or z^3 = 1/27 (18 sqrt(43) - 127)
Taking cube roots gives 1/3 (18 sqrt(43) - 127)^(1/3) times the third roots of unity:
x = 3/4 or z = 1/3 (18 sqrt(43) - 127)^(1/3) or z = -1/3 (-1)^(1/3) (18 sqrt(43) - 127)^(1/3) or z = 1/3 (-1)^(2/3) (18 sqrt(43) - 127)^(1/3)
Substitute each value of z into y = z + 13/(9 z):
x = 3/4 or y = 1/3 (18 sqrt(43) - 127)^(1/3) - (13 (-1)^(2/3))/(3 (127 - 18 sqrt(43))^(1/3)) or y = 13/3 ((-1)/(127 - 18 sqrt(43)))^(1/3) - 1/3 (-1)^(1/3) (18 sqrt(43) - 127)^(1/3) or y = 1/3 (-1)^(2/3) (18 sqrt(43) - 127)^(1/3) - 13/(3 (127 - 18 sqrt(43))^(1/3))
Bring each solution to a common denominator and simplify:
x = 3/4 or y = ((-1)^(1/3) (127 - 18 sqrt(43))^(2/3) - 13 (-1)^(2/3))/(3 (127 - 18 sqrt(43))^(1/3)) or y = 1/3 (13 ((-1)/(127 - 18 sqrt(43)))^(1/3) - (-1)^(1/3) (18 sqrt(43) - 127)^(1/3)) or y = (-(127 - 18 sqrt(43))^(2/3) - 13)/(3 (127 - 18 sqrt(43))^(1/3))
Substitute back for x = y - 4/3:
Answer: x = 3/4 or x = ((-1)^(1/3) (127 - 18 sqrt(43))^(2/3) - 13 (-1)^(2/3))/(3 (127 - 18 sqrt(43))^(1/3)) - 4/3 or x = 1/3 (13 (-1/(127 - 18 sqrt(43)))^(1/3) - (-1)^(1/3) (18 sqrt(43) - 127)^(1/3)) - 4/3 or x = (-(127 - 18 sqrt(43))^(2/3) - 13)/(3 (127 - 18 sqrt(43))^(1/3)) - 4/3
Answer:
-58 i think
Explanation:
-16 - 39 + 16 - 21x = 18 divid 2 -3
-16 - 55 - 39x divided by 2 - 3
-110 divided by 2 - 3
-55 - 3 = -58
We all know that,plants use sunlight for photosynthesis and other live organisms for other purposes also,humans also they use solar panels,they absorb the sunlight
Do the Sunlight get extinct?
Answer:
No, the Sunlight won't get extinct.
Explanation:
It is not true as the sun will not be extinct due to the usage of sunlight by all the living creatures but definitely due to the climatic conditions and several bad activities of humans. It would become extinct or become a red big giant that would destroy the planet.
Scientists have estimated the life on the planet that is 1.5 billion years. Earth would get destroyed much prior to sun. After 7.5 billion years, sun would turn out to be as large as a big giant.
These are the reasons why sun will get extinct but not because of its usage.
A safe is hurled down from the top of a 1.3 x 102 m
building at a speed of 11.0 m/s. What is its velocity as
it hits the ground?
The final velocity is 49.7 m/s downward
Explanation:
The motion of the object is a free fall motion (affected only by the force of gravity), so the object accelerates downward with a constant acceleration of [tex]g=9.8 m/s^2[/tex] (acceleration of gravity). Therefore, we can use the following suvat equation:
[tex]v^2 -u^2 = 2as[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
s is the distance covered
Taking downward as positive direction, we have
u = 11.0 m/s
[tex]a=g=9.8 m/s^2[/tex]
[tex]s=1.3\cdot 10^2 m = 130 m[/tex] (height of the building)
Solving for v, we find the final velocity as the object hits the ground:
[tex]v=\sqrt{u^2+2as}=\sqrt{11.0^2+2(9.8)(120)}=49.7 m/s[/tex]
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What is the quantity of heat energy required to convert 10g cube of ice at -30oC to steam at 120oC. also draw a graph of temperature against energy to show this process.
Answer:
The amount of energy required is 31.1692 kJ .
Explanation:
The transitions of water are as follows,
(243K ice to 273K ice to 273K water to 373k water to 373K steam to 393K steam)
The following required data is,
specific heat capacity of ice= 2.1 kJ/kg
specific heat capacity of water= 4.2 kJ/kg
specific heat capacity of ice= 1.996 kJ/kg
specific latent heat of fusion=334 kJ/kg
specific latent heat of vapourisation = 2260 kJ/kg
FORMULAS:-
temperature change=mc(T2-T1)
phase transistion = mL,
where, m=mass , c=specific heat capacity ,L = latent heat of fusion or vapourisation ,(T2-T1)= temparature change
Thus the total amount of heat is,
=mc(T4-T3) + mL + mc(T3-T2) + mL + mc(T2-T1)
=[tex]10(10^{-3} )(2.1)(30)+10(10^{-3} )(334)+10(10^{-3} )(100)(4.2)+10(10^{-3} )(2260) +10(10^{-3} )(20)(1.996)[/tex]
=(0.3)(2.1) + (3.34) + (4.2) + (22.6) + (0.2)(1.996)
=31.1692 kJ.
Why should people pay attention to scientists when making decisions?
) A. Scientists are always correct.
B. Scientists are the smartest people.
C. Scientists make the best decisions.
D. Scientists use observation and peer review.
SUBMIT
Final answer:
People should pay attention to scientists when making decisions because they utilize an evidence-based process, with observation and peer review, to discern truths about the natural world. The scientific method underpins the reliability of their findings, which can help inform well-grounded decisions.
Explanation:
People should pay attention to scientists when making decisions because scientists use observation and peer review as a part of the scientific method. This process involves making detailed observations, formulating hypotheses, conducting experiments, and drawing conclusions based on evidence. Scientists' claims are supported by evidence that can be examined and experiments that can be replicated, ensuring reliability and validity in their findings.
Additionally, scientists often work in a community where peer-review plays an essential role in validating studies and research before they are widely accepted. Although the process of science may not be perfect due to factors such as human error or bias, the method remains the best we have for systematically understanding the natural world. The iterative nature of science, with its self-correcting mechanisms like peer-review and replication, often leads to a gradual refinement of knowledge.
Therefore, scientists, through their evidence-based approach, are considered reliable sources for informing decisions related to their field of study. Considering science in decision-making processes also ensures that conclusions are rooted in systematically acquired data, as opposed to unfounded claims or assumptions.
Final answer:
Scientists use observation and peer review to ensure the reliability of their findings, making their conclusions more trustworthy than mere opinion or guesswork. Furthermore, science is a democratic and cumulative process, where open debates and the use of systematic data collection lead to continual progress and refinement of knowledge.
Explanation:
People should pay attention to scientists when making decisions because scientists use observation and peer review. This process involves careful measurement, experimentation, and scrutiny by other experts in the field. Through this rigorous method, scientific claims become more reliable and can predict real outcomes more accurately than personal opinions or anecdotes. As our understanding builds upon prior knowledge, we can progress further in our comprehension of the world.
Moreover, science is a democratic process. Scientists must be skeptical and discuss their observations and theories openly, subjecting their findings to the critical analysis of their peers. This discourse allows for the best data to emerge and for errors to be exposed and corrected. Additionally, scientific advancements are cumulative. We learn from past discoveries and then develop new understandings based on the foundations laid by those who came before us.
Political scientists, similar to natural scientists, rely on data to make informed predictions. They use systematic data collection and analysis to understand patterns and make forecasts about future events rather than relying solely on technology or random chance.
Objects 1 and 2 attract each other with a gravitational force of 36.0 units. If the mass of Object 2 is tripled, then the new gravitational force will be _____ units.
Answer:
108N
Explanation:
According to law of gravitation which states that "the force
of attraction between two masses in a gravitational field is directly proportional to the product of their masses and inversely proportional to the square of their distance between them.
Mathematically, F = Gm1m2/r²
Where;
m1 and m2 are the masses of the object
G is the gravitational constant
r is the distance between the masses
If Objects 1 and 2 attract each other with a gravitational force of 36.0 units, we will have;
36 = Gm1m2/r²... (1)
If the mass of Object 2 is tripled, the gravitational force becomes
F = Gm1(3m2)/r²
F = 3Gm1m2/r²... (2)
Dividing equation 1 by 2, we will have;
36/F = {Gm1m2/r²}/3Gm1m2/r²
36/F = Gm1m2/r²×r²/3Gm1m2
36/F = 1/3
Cross multiplying we have
F = 36×3
F = 216N
Therefore, the gravitational force when the second object is tripled is 108N
Final answer:
The new gravitational force, when the mass of Object 2 is tripled and the distance between the objects remains the same, would be 108.0 units.
Explanation:
If the mass of Object 2 is tripled, according to the law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses. The gravitational force can be described by the formula:
F = G \( \frac{m1 \cdot m2}{d²} \)
Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between the centers of the two objects.
In the student's question, if the mass of Object 2 is tripled, and the distance remains unchanged, the new gravitational force would be:
Original force: 36.0 units
New force: 36.0 units \( \times 3\)
New force: 108.0 units
This is because tripling the mass of Object 2 causes the force to triple, as the force is directly proportional to the product of the two masses.
1kg slab of concrete loses 12,000j of heat when it cools from 30 Celsius to 26 Celsius. Determine the specific heat capacity of concrete.
The specific heat capacity of concrete is [tex]3.0 J/(g^{\circ}C)[/tex]
Explanation:
When a certain amount of energy Q is supplied/given off to/from a sample of substance with mass m, the temperature of the substance increases/decreases by an amount [tex]\Delta T[/tex], according to the equation
[tex]Q=mC_s \Delta T[/tex]
where
m is the mass of the substance
[tex]C_s[/tex] is the specific heat capacity of the substance
[tex]\Delta T[/tex] is the change in temperature of the substance
In this problem, we have:
m = 1 kg = 1000 g is the mass of the concrete slab
[tex]Q = -12,000 J[/tex] is the amount of energy lost by the slab
[tex]\Delta T = 30-26= -4^{\circ}C[/tex] is the change in temperature of the slab
Solving the equation for [tex]C_s[/tex], we find the specific heat capacity of concrete:
[tex]C_s = \frac{Q}{m \Delta T}=\frac{-12,000}{(1000)(-4)}=3.0 J/(g^{\circ}C)[/tex]
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Final answer:
The specific heat capacity of concrete is calculated using the heat transfer formula Q = mcΔT, and the given values of 1 kg mass, a temperature change of 4°C, and a heat loss of 12,000 J. The specific heat capacity is found to be 3,000 J/kg/°C.
Explanation:
To determine the specific heat capacity of concrete, we start by using the formula for heat transfer:
Q = mcΔT
where Q is the heat energy transferred (in joules, J), m is the mass (in kilograms, kg), c is the specific heat capacity (in J/kg/°C), and ΔT is the change in temperature (in °C). In this scenario, we are given that a 1kg slab of concrete loses 12,000J of heat when it cools from 30°C to 26°C.
The change in temperature (ΔT) is the final temperature minus the initial temperature, that's 26°C - 30°C = -4°C. We are solving for c, the specific heat capacity of concrete. It is possible to solve for c by rearranging the heat transfer equation:
c = Q / (mΔT)
We substitute the known values into this equation:
c = 12,000 J / (1 kg × -4°C)
c = 12,000 J / -4 kg°C
c = -3,000 J/kg/°C
The negative sign indicates that the concrete is losing heat, however, the specific heat capacity is a positive value. Therefore, the specific heat capacity of concrete is 3,000 J/kg/°C.
the displacement of the body in 5 seconds from the beginning of the motion is
Answer:
The displacement of the object is, d = 5V m
Explanation:
Given data,
The time period of displacement, t = 5 s
Let the average velocity of the object be, V = v m/s
If the object has an initial velocity, V and final velocity v, then the average velocity of the object is,
V = (u + v) / 2
The formula for velocity, displacement and time is,
V = d / t
∴ d = V x t
On substitution,
d = V x 5 s
= 5V m
Substituting the value of V gives the value of displacement,
Thus, the displacement of the object is, d = 5V m
5V m is the displacement of the object.
What is Displacement?Displacement is defined as the change in position of an object. It is represented as an arrow that points from the initial position to the final position.
According to the question,
Time period , t = 5 s
Let, average velocity of the object is V = v m/s
Assume the initial velocity, V and final velocity v,
So, the average velocity of the object is,
[tex]V = \frac{(u + v)}{2}[/tex]
The relationship between velocity, displacement and time is,
[tex]V = \frac{d}{t}[/tex]
[tex]d = V * t[/tex]
Put t =5s
[tex]d = V * 5 s[/tex]
[tex]d = 5V m[/tex]
Therefore,
The displacement of the object is, d = 5V m
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i need help with question 8 and 9
8) The height of the shelf is 2.04 m
9) The gravitational potential energy is 100 J
Explanation:
8)
The gravitational potential energy of an object is given by:
[tex]PE=mgh[/tex]
where
m is the mass of the object
g is the acceleration of gravity
h is the heigth of the object, relative to the ground
For the object in this problem, we have
m = 10 kg
[tex]g=9.8 m/s^2[/tex]
And we know that
PE = 200 J
Therefore we can re-arrange the formula to solve for h, the heigth of the object:
[tex]h=\frac{PE}{mg}=\frac{200}{(10)(9.8)}=2.04 m[/tex]
9)
As before, the gravitational potential energy of the object is given by:
[tex]PE=mgh[/tex]
where in this case, we have:
m = 10 kg is the mass of the object
h = 2.04 m is the height of the object from the ground
While in this case, the acceleration of gravity on this planet is
[tex]g=4.9 m/s^2[/tex]
Substituting,
[tex]PE=(10)(4.9)(2.04)=100 J[/tex]
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So, like my previous question, how do you solve for 4/5 - 1/2?
Answer:
3/10
Explanation:
4/5(2)
-1/2(5)
8/10-5/10
3/10
Answer:
I believe its x = 22
-
Part A
You want to store 1,000 J of energy in an ideal spring when it is compressed by only 2.5 cm. What should be the force constant (spring constant) of this spring?
w
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.
ificant figures.
The energy stored in a spring is
E = 1/2 (k x²)
' k ' is the spring constant . . . the number of newtons of force it takes to stretch or compress the spring by one meter from its relaxed length
' x ' is the distance the spring is stretched or compressed
For this problem, we know ' E ' and ' x ', and we need to find ' k '.
E = 1/2 (k x²)
1,000 = 1/2 (k) (0.025²)
1,000 = 1/2 (k) (0.000625)
Multiply each side by 2 :
2,000 = (k) (0.000625)
Divide each side by 0.000625:
(2,000) / (0.000625) = k
k = 3,200,000
The spring constant is 3.2 x 10⁶ Newtons per meter .
This is a very stiff spring ! My calculator says that if you want to stretch it just 1 inch, you have to pull it with a force of 18,285 pounds ! ! If such a spring exists, it might be used as part of the suspension for a tank or a concrete truck.
The spring constant of the given spring is equal to 3.2 × 10⁶ N/m.
What is Hooke's law?Hooke's law can be explained as a law that states that the force (F) needed to extend or compress a spring by distance linearly with respect to that distance along a straight line.
The spring force can be expressed in the form of an equation:
F = -kx,
where k is a spring constant and x is the possible deformation of the spring. The negative sign indicates that the spring will return to its original shape or position.
The energy stored in the spring when it is compressed is given by:
E = (1/2)kx²
Given, the energy stored in the spring when it is compressed, E = 1000J
The distance by which spring is compressed, x = 2.5 cm = 0.025 m
1000 = (1/2)×k (0.025)²
k = 3.2 × 10⁶N/m
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The diagram shows a student throwing a baseball horizontally at 25 meters per second from a cliff 45 meters above the level ground
Approximately how far from the base of the cliff does the ball hit the ground
The horizontal distance covered by the ball is 75.8 m
Explanation:
The motion of the ball in 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
First of all, we consider the vertical motion to find the time of flight of the ball. Using the suvat equation:
[tex]s=ut+\frac{1}{2}gt^2[/tex]
where
s = 45 m is the vertical displacement of the ball
t is the time of flight
u = 0 is the initial vertical velocity of the ball
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
Solving for t,
[tex]t=\sqrt{\frac{2s}{g}}=\sqrt{\frac{2(45)}{9.8}}=3.03 s[/tex]
Now we know that the ball moves horizontally with a constant velocity of
[tex]v_x = 25 m/s[/tex]
So, the horizontal distance covered by the ball during its flight is
[tex]d=v_x t = (25)(3.03)=75.8 m[/tex]
So the ball lands 75.8 m far from the base of the cliff.
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The ball hits the ground approximately 75.30 meters away from the base of the cliff.
Explanation:
Since the baseball is thrown horizontally, the initial vertical velocity will be zero. The time it takes for the ball to fall can be found using the equation h = (gt^2)/2, where h is the vertical displacement and g is the acceleration due to gravity. Plugging in the values, we get t = sqrt(2h/g). The horizontal distance can be found using the equation d = v*t, where d is the distance and v is the horizontal velocity. Plugging in the values, we get d = v*t. Calculating the values, t = sqrt(2*45/9.8) = 3.01 seconds and d = 25 * 3.01 = 75.30 meters.
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You are standing on the SCALE
The scale is on the floor.
What are the forces on the SCALE?
Answer:
The Normal and Gravitational Force
Explanation:
The normal force pushes up and is between the ground and the scale. The gravitational force is the force exerted on the ground.
es
As the skydiver falls to Earth, she experiences positive acceleration due to
gravity
inertia.
friction
air resistance
Answer:
As the skydiver falls to the Earth, she experiences positive acceleration only due to gravity.
Explanation:
As the skydiver falls to the Earth, she experiences friction in the form of air resistance which tries to slow her down and is proportional to the her velocity. So it cannot have a positive acceleration as it acts in opposite direction to slow her down.
Inertia during skydiving is experienced when we open an parachute, the parachute slows down the speed of are descent hence changing our inertia of motion with a velocity.
Only the Earth's, gravitational field has an positive acceleration as it pulls us towards the Earth, hence increasing our velocity.
2. A car is proceeding at a speed of 14.0 m/s when it collidds with a stationary car in front of it.
During the collision, the first car moves a distance of 3.000 m as it comes tot a stop. The driver
is wearing her seat belt, so she remains in her seat during the collision. If the driver's mass is
52.0 kg, how much force does the belt exert on her during the collision? Neglect any friction
between the driver and the seat.
The force exerted on her is 1700 N
Explanation:
First of all, we start by calculating the acceleration of the car. Since its motion is a uniformly accelerated motion, we can use the following suvat equation:
[tex]v^2-u^2 = 2as[/tex]
where
v = 0 is the final velocity of the car (which comes to a stop)
u = 14.0 m/s is the initial velocity
a is the acceleration
s = 3.0 m is the distance covered by the car during the collision
Solving for a,
[tex]a=\frac{v^2-u^2}{2s}=\frac{0-14^2}{2(3)}=-32.7 m/s^2[/tex]
And the negative sign means it is a deceleration.
Now we can find the force exerted on the passenger during the collision, using Newton's second law:
[tex]F=ma[/tex]
where
F is the force
m = 52.0 kg is the mass of the passenger
[tex]a=32.7 m/s^2[/tex] is the acceleration (we ignore the sign since we are only interested in the magnitude of the force)
Substituting,
[tex]F=(52.0)(32.7)=1700 N[/tex]
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A cat walks 15 m north and then 12 m south. What distance did the cat walk?
O
A. 27 m north
O
B. 3 m
O
c. 27 m
O
D. 3 m north
Answer:
it's 27 meters - answer B