The surface of an incline is coated with an experimental substance that is intended to reduce the frictional force between a blo
ck and the
surface of the incline. A 2 kg block is placed at the top of the incline at a height of 1.8 m, as shown in the figure. After the block is released
from rest, the block slides down the incline and a motion detector at the bottom of the incline measures the block's speed as 5.8 after the
block is no longer on the incline. Which of the following claims is correct about the experimental substance?
The experimental substance reduced all the frictional force because all the gravitational potential energy of the Earth-block
system at the top of the incline was converted into the kinetic energy of the block at the bottom of the incline.
The experimental substance did not reduce all the frictional force because some of the gravitational potential energy of the
Earth-block system at the top of the incline was converted into nonmechanical energy
с
The effectiveness of the experimental substance cannot be determined because the speed of the block at the bottom of the
inline, as measured by the motion detector, indicates that the block has more energy at this location than the Earth-block
system had at the top of the incline.
D
The effectiveness of the experimental substance cannot be determined without knowing the magnitude of the frictional
force between the block and the incline before and after the experimental substance was applied to the incline.
Lo
surface of the incline. A 2 kg block is placed at the top of the incline at a height of 1.8 m, as shown in the figure. After the block is released
from rest, the block slides down the incline and a motion detector at the bottom of the incline measures the block's speed as 5.8 after the
block is no longer on the incline. Which of the following claims is correct about the experimental substance?
The experimental substance reduced all the frictional force because all the gravitational potential energy of the Earth-block
system at the top of the incline was converted into the kinetic energy of the block at the bottom of the incline.
The experimental substance did not reduce all the frictional force because some of the gravitational potential energy of the
Earth-block system at the top of the incline was converted into nonmechanical energy
с
The effectiveness of the experimental substance cannot be determined because the speed of the block at the bottom of the
inline, as measured by the motion detector, indicates that the block has more energy at this location than the Earth-block
system had at the top of the incline.
D
The effectiveness of the experimental substance cannot be determined without knowing the magnitude of the frictional
force between the block and the incline before and after the experimental substance was applied to the incline.
Lo
2 answers:
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a) The speed of the block at a height of 0.25 m is 2.38 m/s
b) The compression of the spring is 0.25 m
c) The final height of the block is 0.54 m
Explanation:
a)
We can solve the problem by using the law of conservation of energy. In fact, the total mechanical energy (sum of kinetic+gravitational potential energy) must be conserved in absence of friction. So we can write:
where
is the initial potential energy, at the top
is the initial kinetic energy, at the top
is the final potential energy, at halfway
is the final kinetic energy, at halfway
The equation can be rewritten as
where:
m = 2.7 kg is the mass of the block
is the acceleration of gravity
is the initial height
u = 0 is the initial speed
is the final height of the block
v is the final speed when the block is at a height of 0.25 m
Solving for v,
b)
The total mechanical energy of the block can be calculated from the initial conditions, and it is
At the bottom of the ramp, the gravitational potential energy has become zero (because the final heigth is zero), and all the energy has been converted into kinetic energy. However, then the block compresses the spring, and the maximum compression of the spring occurs when the block stops: at that moment, all the energy of the block has been converted into elastic potential energy of the spring. So we can write
where
k = 453 N/m is the spring constant
x is the compression of the spring
And solving for x, we find
c)
If there is no friction acting on the block, we can apply again the law of conservation of energy. This time, the initial energy is the elastic potential energy stored in the spring:
while the final energy is the energy at the point of maximum height, where all the energy has been converted into gravitational potetial energy:
where is the maximum height reached. Solving for this quantity, we find
which is the initial height: this is correct, because the total mechanical energy is conserved, so the block must return to its initial position.
Learn more about kinetic and potential energy:
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