Question
A fan is attached to the top of a block, as shown. The block is released from rest at the top of a ramp and the fan exerts a constant force on the block opposite the block's direction of motion. The block slides a distance along the ramp and then transitions to a horizontal surface, eventually coming to rest momentarily after traveling a distance . Frictional forces are negligible. Which of the following correctly describes the relationship between and ?
(A) must be less than .
Studdy Solution
STEP 1
1. The block is released from rest.
2. The fan exerts a constant force opposite to the block's direction of motion.
3. Frictional forces are negligible.
4. The block slides down a ramp and then onto a horizontal surface.
5. The block comes to rest after traveling a distance on the horizontal surface.
STEP 2
1. Analyze the forces acting on the block.
2. Determine the energy transformations involved.
3. Compare the distances and .
STEP 3
The block is subject to gravitational force down the ramp and a constant opposing force from the fan.
STEP 4
Initially, the block has potential energy at the top of the ramp. As it slides down, this potential energy is converted into kinetic energy.
The fan exerts a constant force, doing negative work on the block, reducing its kinetic energy.
STEP 5
When the block reaches the horizontal surface, it has kinetic energy reduced by the work done by the fan.
On the horizontal surface, the fan continues to exert a force, further reducing the block's kinetic energy until it comes to rest.
STEP 6
The work done by the fan on the ramp and on the horizontal surface is equal to the kinetic energy the block had at the bottom of the ramp.
Since the fan exerts a constant force, the distance on the horizontal surface, where the block comes to rest, must be less than , because the block starts with less kinetic energy on the horizontal surface than it had at the bottom of the ramp.
The correct relationship is:
(A) must be less than .
Was this helpful?
