Voltage differences create an electric field that pushes free charges through a conductor, resulting in an electric current. This occurrence is explained by Ohm's Law, which states that current is directly proportional to the voltage applied to a conductor. Conventional current flows from the positive to the negative terminal although electrons, the actual charge carriers in metals, move in the opposite direction.
Explanation:Voltage differences are what drive an electric current in a conductor. When a voltage source such as a battery or a generator is connected to a conductor, it applies a potential difference that creates an electric field. This electric field exerts a force on free charges, causing them to move and create an electric current. In a material like a metal wire, the current is carried by the movement of electrons, which are negative charges moving from the negative terminal to the positive terminal. When discussing current flow, we often refer to the term "conventional current," which flows from the positive terminal to the negative terminal, even though the actual charge carriers (electrons) move in the opposite direction. This stems from historical convention initiated by Benjamin Franklin.
According to Ohm's Law, the current that flows through a substance is directly proportional to the voltage applied to it, which means that a higher voltage will generally result in a larger current, assuming the resistance of the material does not change. If charges accumulate at certain points, reducing the voltage there, the electric field will adjust to push the current toward areas with higher voltage. In static conditions, excess charges collect along the surface of a conductor until static equilibrium is reached.
a cheetah ran 100 meters in 6 seconds. what is its average speed?
Answer:
A=16.6 repeating
explanation:
take 100/6 and solve just make sure your equation is set up correctly!
and you should get an answer of 16.6 repeating or 166 m/hour or 16.6 meters/per/hour
If a cheetah ran 100 meters in 6 seconds, then the average speed of the cheetah would be 16.67 meters per second.
What is speed?The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object.
As given in the problem a cheetah ran 100 meters in 6 seconds , then we have to find the average speed of the cheetah,
The distance traveled by the cheetah = 100 meters
The time is taken by the Cheetah to cover the distance = 6 seconds
The average speed of the cheetah = 100 / 6
= 16.67 meters per second
Thus, If a cheetah ran 100 meters in 6 seconds, then the average speed of the cheetah would be 16.67 meters per second.
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A thread holds two carts together on a frictionless surface. A spring is compressed
between the two carts. After the thread between the two carts is cut the cart on the
left with a mass of 1.5 kg moves away with a velocity of 27 cm/s. What is the
velocity of the cart on the right that has a mass of 4.5 kg? thisss is the answer I just need to show work>>>>>>>(0.09 m/s)
Answer:
Velocity on the right side of the cart [tex]=0.09\ ms^{-1}[/tex]
Explanation:
Given
⇒The mass on the left of the cart [tex]m_1=1.5\ kg[/tex]
Its velocity [tex]v_1=27\ cm/s[/tex],[tex]v_1=\frac{27}{100}=0.27\ m/s[/tex]
⇒Mass on the right of the cart [tex]m_2=4.5\ kg[/tex]
Velocity[tex]=?[/tex] We have to find [tex]v_2[/tex]
From
The law of conservation of linear momentum:
We can say that.
Initial momentum will equalize the final momentum.
And momentum is the product of mass and its velocity.
Assigning one of its velocity as negative because both are in different direction.
Lets call [tex]v_1=-0.27m/s[/tex]
Recalling the formula and plugging the values.
[tex]m_1(-v_1)+m_2v_2=0[/tex]
[tex]v_2=-\frac{m_1(-v_1)}{m_2} =-\frac{1.5\times -0.27}{4.5} =0.09\ m/s[/tex]
So the velocity of the cart on the right side that has a mass of [tex]4.5\ kg[/tex] is [tex]0.09\ ms^{-1}[/tex]
Using the principle of conservation of momentum, the velocity of the right cart is calculated to be 0.09 m/s.
To determine the velocity of the right cart, we can use the principle of conservation of momentum. According to this principle, the total momentum of a closed system remains constant if no external forces act on it.Given:
Mass of the left cart ([tex]m_1[/tex]) = 1.5 kgVelocity of the left cart ([tex]v_1[/tex]) = 27 cm/s = 0.27 m/sMass of the right cart ([tex]m_2[/tex]) = 4.5 kgInitial total momentum = 0 (since both carts start from rest)Let [tex]v_2[/tex] be the velocity of the right cart after the thread is cut. By conservation of momentum:Step-by-Step Calculation:
Write the initial momentum equation:
([tex]m_1[/tex] + [tex]m_2[/tex]) * 0 = [tex]m_1[/tex] * [tex]v_1[/tex] + [tex]m_2[/tex] * [tex]v_2[/tex]Simplify the equation:
0 = (1.5 kg * 0.27 m/s) + (4.5 kg * [tex]v_2[/tex])Solve for v2:
4.5 * [tex]v_2[/tex] = - 0.405[tex]v_2[/tex] = -0.09 m/sThe negative sign indicates that the right cart moves in the opposite direction to the left cart. Hence, the velocity of the cart on the right is 0.09 m/s.
What assumption do error theorist claims at the heart of morality
Answer:
a) The assumption that error theorists claim is at the heart of morality is that sincere moral judgments are always in error, therefore there is no moral knowledge possible.
Explanation:
How is a gas affected when pressure, temperature, or volume
change?
Explanation:
I never really took physics yet, but I do have some general knowledge of particle physics.
When pressure increases, the gas molecules will get closer together and rise in temperature, vice versa. (That's actually one way we get energy. The more pressure we apply to gas, the hotter it gets and therefore releases pretty good amounts of energy)
When temperature increases, the gas molecules will try to get away from each other and spread out, vice versa. The higher the temperature, the faster the particles move
And when volume increase, there is more room for the gas particles to bounce around and they are generally spread out from each other.
Someone else can answer if I didn't explain it correctly
Answer:
The volume of a given gas sample is directly proportional to its absolute temperature at constant pressure (Charles's law). The volume of a given amount of gas is inversely proportional to its pressure when temperature is held constant (Boyle's law).
Explanation:
10. Which of the following is an acceleration?
a. 12 m/s2 down
b. 5 m/s up
c. 8N West
Answer:
a. 12 m/s² down
Explanation:
Acceleration has units of length per time squared. Acceleration is a vector, so it also has a direction.
Objects in motion tend to stay in _____ motion at a _____ speed, if no unbalanced forces are acting on them.
A. curved; variable
B. curved; constant
C. straight-line; variable
D. straight-line; constant
Objects in motion tend to stay in straight-line motion at a constant speed, if no unbalanced forces are acting on them
(option: D. straight-line; constant)
Explanation:
This statement is exactly summarized by Newton's first law of motion, which states that:
"For an object moving by uniform motion (=at constant velocity or at rest), the object will maintain its uniform motion if no unbalanced forces act on it".
This law essentially tells that if there is an object at rest, this will not move unless some external (unbalanced) force is applied on it, and if the object is moving by uniform motion (=constant speed in a straight line), it will continue moving with this motion unless some external (unbalanced) force is applied on it.
This law is generally difficult to prove in real-life situation, because there are always some unbalanced forces acting on objects. For instance, if we roll a ball along a table, if we neglect the friction between the table and the ball, the ball will continue moving with uniform motion forever. Of course this does not occur in real life, only because there is an external (unbalanced) force, the friction, that makes the ball slowing down and eventually stop.
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a 3,000 kg car is traveling with a constant velocity of 10 m/s. how much work must be applied to the car to change its speed to 15 m/s?
187500 Joules of work must be done to the 3000 kg car to change its speed from 10 m/s to 15 m/s.
Explanation:
Work is the measurement of the force on an object that overcomes a resisting force (such as friction or gravity) times the distance the object is moved. If there is no distance, there is no work, no matter what the effort.
Work done = Force * displacement
When you apply enough force on an object to overcome a resistive force, such that you move that object, you are doing work on that object. There is a relationship between that work and mechanical energy.
When an object is accelerated, you are doing work against inertia, such that the work equals the change in kinetic energy of the object.
Work done = Change in K.E
In the given case:
mass = m = 3000 kg
initial velocity = v₁ = 10 m/s
final velocity = v₂ = 10 m/s
Work = W = (1/2)m(v₂)² - (1/2)m(v₁)²
[tex]= \frac{1}{2}m(v2^{2} - v1^2)\\= \frac{3000}{2}(15^{2} - 10^{2})\\= 1500(225 - 100)\\= 1500*125\\= 187500 kg m^{2}s^{-2} \\= 187500 Nm\\= 187500 J[/tex]
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Assume that a hockey player skates 60 feet in 3 seconds. What is the player’s speed? If the hockey player travels this distance from East to West, what is his velocity?
Answer:
20ft/secs
Explanation:
60 feet/ 3 secs
What are possible units for impulse? Check all that apply.
Okg•m
Okg.
ONós
ON•m
O Nom
The units for impulse are
[tex]N\cdot s[/tex]
Explanation:
We have two definition for impulse:
1) Impulse is defined as the product between the force exerted on an object and the time interval during which the force is applied:
[tex]I=F \Delta t[/tex]
where
F is the force, measured in Newtons (N)
[tex]\Delta t[/tex] is the time interval, measured in seconds (s)
From this definition it follows that Impulse can be measured in [tex]N\cdot s[/tex], which corresponds to option 3)
2)
Impulse is also defined as the change in momentum of an object:
[tex]I=\Delta p[/tex]
where
[tex]\Delta p[/tex] is the change in momentum of the object
The change in momentum has the same units of the change in momentum, so [tex]kg \cdot m \cdot s^{-1}[/tex], which corresponds to none of the options given
So the only correct option is
[tex]N\cdot s[/tex]
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a 2-kg bowling ball is 2.5 meters off the ground on a post when it falls. Just before it reaches the ground, it is traveling 7 m/s. Assuming tht there is no air resistance, which statement is true? 1. the initial potential energy is greater than the final kinetic energy 2. the mechanical energy is conserved 3. the mechanical energy is not conserved 4. the initial potential energy is less than the final kinetic energy
“The mechanical energy is conserved" in the given system is true out of all given options.
Answer: Option 2
Explanation:
According to law of conservation of energy, the energy will neither be created nor be destroyed, irrespective of the type of energy. As in the present case, the ball is bowled and it is travelling to ground, so the mechanical energy is working in this case. Thus the mechanical energy will be conserved. Even it can be shown as follows.
As the 2 kg ball is travelling with a speed of 7 m/s, the kinetic energy exhibited by the ball while falling to ground will be
[tex]\text {Kinetic energy}=\frac{1}{2} \times \text { mass of the ball } \times\left(\text { speed of the ball) }^{2}\right.[/tex]
Thus, applying given values, we get,
[tex]\text {Kinetic energy exhibited by the ball}=\frac{1}{2} \times 2 \times 7 \times 7=49 \mathrm{J}[/tex]
Similarly, as the ball is 2.5 m above ground, the potential energy will also be exhibited by the ball at that position. So the potential energy will be
[tex]\text {Potential energy}=\text {Mass} \times \text {acceleration} \times \text {height}[/tex]
Thus,
[tex]\text { Potential energy exhibited by the ball }=2 \times 9.8 \times 2.5=49 \mathrm{J}[/tex]
Thus as the magnitude of kinetic energy is equal to the magnitude of potential energy exhibited by the ball with varying direction, the net energy will be zero. This is because the kinetic energy will be acting in opposite direction to the potential energy exhibited by the ball. Hence as the net energy is zero, the mechanical energy is conserved.
two objects were lifted by a machine. One object had a mass of 2 kilograms, was lifted at a speed of 2m/sec . The other had a mass of 4 kilograms and was lifted at 3m/sec. Which object had more kinetic energy while it was being lifted? Show all calculations
Object 2 has more kinetic energy
Explanation:
The kinetic energy of an object is the energy possessed by the object due to its motion, and it is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m is the mass of the object
v is its speed
In this problem, for object 1:
m = 2 kg
v = 2 m/s
So its kinetic energy is
[tex]K_1 = \frac{1}{2}(2)(2)^2=4 J[/tex]
For object 2,
m = 4 kg
v = 3 m/s
So its kinetic energy is
[tex]K_2 = \frac{1}{2}(4)(3)^2=18 J[/tex]
Therefore, object 2 has more kinetic energy.
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How much heat is lost when 10 g of Glass cools 15 Celsius
The heat lost by the glass is 126 J
Explanation:
The amount of heat lost by a substance is proportional to the change in temperature of the substance according to the following equation:
[tex]Q=mC_s \Delta T[/tex]
where
Q is the amount of heat lost
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
In this problem, we have:
m = 10.0 g is the mass of the glass
[tex]\Delta T = -15^{\circ}C[/tex] is the change in temperature of the glass
[tex]C_s = 0.840 J/g{\circ}C[/tex] is the specific heat capacity of glass
Substituting and solving for Q, we find
[tex]Q=(10)(0.840)(-15)=-126 J[/tex]
So, the heat lost by the glass is 126 J.
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The heat loss for 10 g cooling by 15 °C can be calculated; the result would be -126 J.
To find out how much heat is lost when 10 g of glass cools by 15 °C, one would need to know the specific heat capacity of glass and use the formula: Q = mcΔT, where 'Q' is the quantity of heat, 'm' is the mass, 'c' is the specific heat capacity, and 'ΔT' is the change in temperature. Unfortunately, the specific heat capacity of glass is not provided in the question or the examples, which is necessary to calculate the exact amount of heat lost. However, for illustration, if we assume a typical value for glass is approximately 0.84 J/g°C, the calculation for the heat lost would be: Q = 10 g × 0.84 J/g°C × (-15 °C) = -126 J (negative sign indicating loss).
if 2.0 J of work is done in raising a 180 g apple, how far is it lifted
Answer:
1.14 meters
Explanation:
You have already learned that work and energy have same units i.e. Joule (J).
If the object has travelled some distance (upwards) then there must be some potential difference (increased potential energy).
Thus the energy needed to lift the ball can be found by this formula:
E
p
=
m
⋅
g
⋅
h
Where
E
p
means potential energy needed (or simply work done). m stands for mass, g for gravitational energy, and h for the height reached.
Now we know the energy(2 J), the mass (0.18 kg), and gravitational energy (9.8 m/s^2). Putting into the formula we get:
2
=
0.18
⋅
9.8
⋅
h
2
0.18
⋅
9.8
=
h
2
1.76
=
h
1.14
=
h
Finally,
height reached above the ground = 1.14 m
A motorcycle begins at rest and accelerates uniformly S7.9 we want to find a time to take the motorcycle to reach a speed of 100 which chimeric formula would be most useful to solve for the target unknown
The motorbike reaches 100 km/h in 3.5 seconds
Explanation:
The motion of the motorbike is a uniformly accelerated motion (= constant acceleration), therefore we can use the following suvat equation:
[tex]v=u+at[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
For the motorbike in this problem,
u = 0 (it starts from rest)
[tex]v = 100 km/h = 27.8 m/s[/tex] is the final velocity
[tex]a=7.9 m/s^2[/tex] is the acceleration
Solving for t, we find the time it takes for the bike to reach that velocity:
[tex]t=\frac{v-u}{a}=\frac{27.8-0}{7.9}=3.5 s[/tex]
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A motorbike is travelling with a velocity of 3m/s. It accelerates at a rate of 9.3m/s for 1.8s. Calculate the distance it travels in this time
Explanation:
Consider the kinematic equation,
[tex]x = vt + \frac{1}{2} a {t}^{2} [/tex]
where x is the distance traveled, v is the initial velocity, a is the acceleration and t is time. By plugging in known values and solving for x,
[tex]x = 3(1.8) + \frac{1}{2} (9.3) {1.8}^{2} [/tex]
through simple algebra we get
[tex]x = 20.466[/tex]
where this is the distance traveled in meters.
When reporting the speed, we need to include the value, units and direction the object was traveling.
True or False??
Answer:
When reporting the speed, we need to include the value, units and direction the object was traveling.
It is a FALSE
Explanation:
Justification :
Speed is a scalar quantity.Scalar quantity required only magnitude not the direction.The definition of speed is total distance travelled divided by total time taken to cover that distance.Therefore, speed required value and units not the direction.By velocity which is similar to speed required value, units and direction. And velocity is a vector quantity hence it require direction.For example without speed of a car is 50 m/s. Here 50 is the value and m/s is the unit of a speed.Starting from rest, a 75.0-kg snowboarder slides straight down a 115-m slope in 6.6 s. If the slope is a 35°
incline, find the following:
(a) The acceleration of the snowboarder.
The acceleration of the snowboarder is [tex]5.6 m/s^2[/tex] down along the incline
Explanation:
To find the acceleration of the snowboard, we have to analyze the forces acting along the direction parallel to the incline.
There is only one force acting in this direction, and it is the component of the weight parallel to the incline, given by
[tex]mg sin \theta[/tex]
where
m = 75.0 kg is the mass of the man
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]\theta=35^{\circ}[/tex] is the angle of the incline
Substituting, we find that the net force along the incline is:
[tex]F=(75.0)(9.8)(sin 35^{\circ})=421.6 N[/tex]
According to Newton's second law, the net force on the snowboard is equal to the product between his mass and his acceleration:
[tex]F=ma[/tex]
where a is the acceleration. Therefore, solving for a, we find
[tex]a=\frac{F}{m}=\frac{421.6}{75}=5.6 m/s^2[/tex]
And the direction of this acceleration is down along the incline.
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When a cup is placed on a table, which force prevents the cup from falling to the ground?
Answer:Answer: Normal force prevents the cup from falling to the ground. Explanation : When a cup is placed on a table, the forces acting on the cup are the gravitational force and the normal force. The gravitational force acts in the downward direction while the normal force acts in an upward direction
Explanation:
Different measurements are expressed in different units. Choose the correct SI units for the following types of
measurement
The SI units for measuring the velocity of the car:
The SI units for measuring the acceleration of the car:
The SI units for measuring force:
The SI units for measuring mass:
Answer: I don't know why people just cant give a straight answer.
Meters per second
Meters per second Squared
Newtons
Kilograms
100% right keep it going.
Explanation:
The S.I. units for measuring the velocity, acceleration, force, and mass are meter per second (m/s), meter per second squared (m/s²), Newton (N), and Kilogram (Kg) respectively.
What is the International System of Units?The International System of Units or S.I. units can be described as the modern version of the metric system and the world's most globally used system of measurement which is established and controlled by the Conference on Weights and Measures.
S.I. units system can be described as a system of measurement used in every country in the world employed in technology, industry, science, and commerce.
The S.I. exhibits a coherent system of units starting with seven base units. The second (s, the unit of time), Kilogram (kg, unit of mass), meter (m, length), kelvin (K, unit of temperature), mole (mol, amount of substance), ampere (A, unit of electric current), and candela (cd, luminous intensity).
Velocity is the ratio of distance and time so it has an S.I. unit of meter per second. Acceleration is the ratio of velocity and time so it has an S.I. unit of meter per second squared.
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3. The angular dispersion of a prism depends on
A. the index of refraction only B. the angle of
incidence as well as the index of refraction C. the
angle of incidence only D. the hi thickness of the
prism E, the prism angie.
Answer:
The angular dispersion of a prism depends on the index of refraction only.
Explanation:
The angular dispersion of a prism mainly depends upon the refractive index of a material. And this refractive index is dependent on the wavelength of light. Each colour possesses its own characteristic and the wavelength is also different. There has been a relation between refractive index of a material and wavelength of light higher the wavelength of the colour, greater would be the dispersion of light. As like when we passes light from a prism, according to this principle, the colours are dispersed.
All the other options are incorrect as cannot decide angle of dispersion.
From the choices below, choose all that are correct.
I. Sound traveling faster through the air in the Sahara desert than in Antarctica.
II. An astronaut hearing the loud explosion of a ship from a mile away in space.
III. Speeds and frequencies of sounds change as they pass through different mediums.
A) I
B) I and II
C) I and III
D) II and III
The correct choice is
A) I. Sound traveling faster through the air in the Sahara desert than in Antarctica.
Explanation:
Sound is a mechanical wave, which is a periodic disturbance of the space that propagates through vibrations of the particles in the medium filling the space. In particular, sound waves are longitudinal waves, in which the direction of oscillation of the particles in the medium is parallel to the direction of propagation of the wave.
Let's analyze now each statement:
I. Sound traveling faster through the air in the Sahara desert than in Antarctica. --> TRUE. In fact, the higher the temperature of the air, the faster the sound propagates. In particular, there is a linear relationship between speed of sound and temperature of the air:
[tex]v=331.3 + 0.6T(^{\circ}C)[/tex]
where [tex]T(^{\circ}C)[/tex] is the temperature of the air in Celsius degrees.
II. An astronaut hearing the loud explosion of a ship from a mile away in space. --> FALSE. This is not possible: in fact, sound is a mechanical wave, so it propagates only through a medium, and it cannot propagate in a vacuum (space is essentially vacuum, so sound cannot propagate in space).
III. Speeds and frequencies of sounds change as they pass through different mediums. --> FALSE. When a wave passes through different mediums, only the speed and the wavelength of the wave change, while the frequency remains the same.
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Answer: I. Sound traveling faster through the air in the Sahara desert than in Antarctica.
Explanation:
Frequency stays the same as sound passes through different mediums. An explosion in space is not going to be heard if you are in the vacuum of space yourself.
Choose the FALSE statement about an object that has mass. A. It has volume. B. It must be heavy. C. It takes up space. D. It is made of matter.
Answer:
B. It must Be Heavy
Explanation:
An Object Can Have Mass And Be Light Such As A Pencil
To sterilize a 53.0 g glass baby bottle, we must raise its temperature from 25.0°C to 92.0°C. How much heat transfer (in J) is required?
The heat energy required is 2983 J
Explanation:
When an amount of energy Q is supplied to a certain sample of substance of mass m, the temperature of the substance increases by an amount of [tex]\Delta T[/tex] according to the equation :
[tex]Q=mC_s \Delta T[/tex]
where
Q is the heat supplied
m is the mass of the object
[tex]C_s[/tex] is the specific heat capacity of the substance
[tex]\Delta T[/tex] is the change in temperature
For the glass bottle in this problem:
[tex]m=53.0 g[/tex]
[tex]\Delta T = 92.0 - 25.0 =67.0^{\circ}C[/tex] is the change in temperature
[tex]C_s = 0.84 J/g^{\circ}C[/tex] is the specific heat of glass
Substituting into the equation, we find
[tex]Q=(53.0)(0.84)(67)=2983 J[/tex]
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You pull a suitcase along the floor by exerting 43N at an angle. The force of friction is 27 N and the suitcase moves at a constant speed. What angle does the handle make with the horizontal?
The angle of the force is [tex]51.1^{\circ}[/tex]
Explanation:
To solve this problem, we can apply Newton's second law along the horizontal direction of motion of the suitcase:
[tex]\sum F_x = ma_x[/tex]
where
[tex]\sum F_x[/tex] is the net force along the x-axis
m is the mass of the suitcase
[tex]a_x[/tex] is the acceleration along the x-axis
The suitcase is moving at constant speed, so the acceleration is zero:
[tex]a_x=0[/tex]
Therefore the net force must also be zero:
[tex]\sum F_x = 0[/tex] (1)
We have two forces acting along the horizontal direction:
- The component of the push (forward) in the horizontal direction, [tex]F cos \theta[/tex], with
F = 43 N
[tex]\theta[/tex] = angle of the force with the horizontal
- The force of friction, [tex]F_f = 27 N[/tex], backward
So the net force can be written as
[tex]\sum F_x = F cos \theta - F_f[/tex] (2)
Combining (1) and (2),
[tex]F cos \theta - F_f = 0[/tex]
And so we can find the angle:
[tex]\theta = cos^{-1}(\frac{F_f}{F})=cos^{-1}(\frac{27}{43})=51.1^{\circ}[/tex]
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A celebrated Mark Twain story has motivated contestants in the Calaveras County Jumping Frog Jubilee, where frog jumps as long as 2.20 m have been recorded. If a frog jumps 2.20 m and the launch angle is 54.0°, find the frog's launch speed and the time the frog spends in the air. Ignore air resistance.
(a) the frog's launch speed (in m/s)
(b)the time the frog spends in the air (in s)
Answer:
[tex]v_0[/tex]=4.761 m/s
t=0.786 sec
Explanation:
In a projectile motion (or 2D motion), the object is launched with an initial angle [tex]\theta[/tex] and an initial velocity [tex]v_0[/tex]
The components of the velocity are
[tex]v_{ox}=v_ocos\theta[/tex]
[tex]v_{oy}=v_osin\theta[/tex]
Similarly the displacement has the components
[tex]x=v_{ox}.t=v_ocos\theta.t[/tex]
[tex]y=v_osin\theta.t-\frac{gt^2}{2}[/tex]
The last formula is valid only if the object is launched at ground level, as our frog does.
There are two times where the value of y is zero, when t=0 (at launching time) and when it lands back from the air. We need to find that time t by making y=0
[tex]0=v_osin\theta.t-\frac{gt^2}{2}[/tex]
Dividing by t (assuming t different from zero)
[tex]0=v_osin\theta-\frac{gt}{2}[/tex]
Then we find the total flight as
[tex]t=\frac{2v_osin\theta}{g}[/tex]
Replacing this time in the formula of x
[tex]x=v_ocos\theta\frac{2v_osin\theta}{g}[/tex]
We can solve for [tex]v_o[/tex]
[tex]\displaystyle v_0=\sqrt{\frac{xg}{sin2\theta}}[/tex]
Knowing that x=2.20 m and [tex]\theta=54[/tex]°
[tex]\displaystyle v_0=\sqrt{\frac{xg}{sin2\theta}}=4.761m/s[/tex]
We now compute t
[tex]t=\frac{2v_osin\theta}{g}=0.786\ sec[/tex]
Final answer:
The launch speed of the frog is 4.81 m/s, and the time the frog spends in the air is 0.737 seconds.
Explanation:
A) Using the kinematic equation for projectile motion, we can find the launch speed. The launch speed, in this case, would be 4.81 m/s.
B) To determine the time the frog spends in the air, we can use the time of flight formula for projectile motion. The time in the air for the frog is 0.737 seconds.
A liquid mixture of water and alcohol has a density of 900kg/m3. find the mass of alcohol in one litre of the mixture
Answer:
900 grams
Explanation:
NB: 1litres=1000ml
Density=mass/volume
900kg/m³=mass/1000ml
mass =900kg/m³×100ml
mass=900grams
The mass of the alcohol in one liter of the mixture must be less than or equal to 0.9 kg, given that the density of the mixture is 0.9 kg/liter.
Explanation:The key point to remember here is that the density of a solution is the ratio of its mass to its volume. Here, we are given that the density of the water-alcohol mixture is 900 kg/m3. Note that 1 m3 is equal to 1000 liters, so the density can also be expressed as 900 kg/1000 liters, or 0.9 kg/liter.
Since the question asks for the mass of the alcohol in one liter of the solution, and assuming that the entire liter is made up of the solution without any empty space, the mass of the solution in one liter would be 1 liter * 0.9 kg/liter = 0.9 kg.
Therefore, the mass of alcohol in one liter of the mixture must be less than or equal to 0.9 kg, assuming none of the mass is from any other substance. In order to find the exact mass of the alcohol, additional information would be required such as the ratio of water to alcohol in the mixture.
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if f(x)=4/x+2 and g is the inverse of f,then g'(10)=
Answer:
g'(10) = [tex]\frac{-1}{16}[/tex]
Explanation:
Since g is the inverse of f ,
We can write
g(f(x)) = x (Identity)
Differentiating both sides of the equation we get,
g'(f(x)).f'(x) = 1
g'(10) = [tex]\frac{1}{f'(x)}[/tex] --equation[1] Where f(x) = 10
Now, we have to find x when f(x) = 10
Thus 10 = [tex]\frac{4}{x}[/tex] + 2
[tex]\frac{4}{x}[/tex] = 8
x = [tex]\frac{1}{2}[/tex]
Since f(x) = [tex]\frac{4}{x}[/tex] + 2
f'(x) = -[tex]\frac{4}{x^{2} }[/tex]
f'([tex]\frac{1}{2}[/tex]) = -4 × 4 = -16
Putting it in equation 1, we get:
We get g'(10) = -[tex]\frac{1}{16}[/tex]
why don't we use more renewable energy sources
Answer:
Renewable energy sources 1.Cost more then nonrenewable resources and 2.Are so far not as reliable as nonrenewable energy.
Explanation:
renewable energy often has trouble creating the same amount of power that fossil fuels make because of its efficiency , they're expensive too
I am driving 65 mph when I suddenly come to a stop. my acceleration was -9.2 m/s squared. how long did it take me to stop?
hint: convert mph to m/s first
The car takes 3.15 s to stop
Explanation:
The motion of the car is a uniformly accelerated motion (=constant acceleration), therefore we can use the following suvat equation:
[tex]v=u+at[/tex]
where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
Keeping in mind that
1 mile = 1609 metres
1 hour = 3600 seconds
Here we have:
[tex]u = 65 mph \cdot \frac{1609 m/mile}{3600 s/hour}=29.0 m/s[/tex] is the initial velocity, converted into m/s
v = 0 is the final velocity (the car comes to a stop)
[tex]a=-9.2 m/s^2[/tex] is the acceleration
And solving the equation for t, we find
[tex]t=\frac{v-u}{a}=\frac{0-29.0}{-9.2}=3.15 s[/tex]
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If a car is traveling with a constant velocity of 20m/s westward, what is the net force acting on a car
The net force on the car is zero
Explanation:
We can answer this question by applying Newton's second law of motion. In fact, we have:
[tex]\sum F = ma[/tex]
where
[tex]\sum F[/tex] is the net force acting on an object
m is the mass of the object
a is its acceleration
In this problem, the car is travelling with a constant velocity: this means that the acceleration of the car is zero (because acceleration is the rate of change of velocity). Therefore,
[tex]a=0[/tex]
So the equation becomes
[tex]\sum F = 0[/tex]
which means that the net force on the car is zero.
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