Suppose the block in the previous problem were launched with the same initial speed on the following frictionless ramps. In each case state whether the magnitude of the net work done on the block from the bottom to the top of the ramp is greater than, less than, or equal to the magnitude of the net work done on the block in problem 2. Explain your answer in each case. ja Case a a. The ramp is steeper (a>0). H Case b b. The ramp has two sections of different slope. Case c c. The ramp has several sections of gradually increasing steepness. Case d d. The ramp is curved. Use the work-energy theorem to rank the final speeds of the block on the ramps (a-d), assuming the block is launched with the same initial speed in each case. If the final speeds are the same in any of the cases, state that explicitly. Explain.
Suppose the block in the previous problem were launched with the same initial speed on the following frictionless ramps. In each case state whether the magnitude of the net work done on the block from the bottom to the top of the ramp is greater than, less than, or equal to the magnitude of the net work done on the block in problem 2. Explain your answer in each case. ja Case a a. The ramp is steeper (a>0). H Case b b. The ramp has two sections of different slope. Case c c. The ramp has several sections of gradually increasing steepness. Case d d. The ramp is curved. Use the work-energy theorem to rank the final speeds of the block on the ramps (a-d), assuming the block is launched with the same initial speed in each case. If the final speeds are the same in any of the cases, state that explicitly. Explain.
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Transcribed Image Text:s Suppose the block in the previous problem were launched with
the same initial speed on the following frictionless ramps. In
each case state whether the magnitude of the net work done on
the block from the bottom to the top of the ramp is greater
than, less than, or equal to the magnitude of the net work done
on the block in problem 2. Explain your answer in each case.
Case a
a. The ramp is steeper (a>0).
H
1B
Case b
b. The ramp has two sections of different slope.
Case c
c. The ramp has several sections of gradually increasing
steepness.
Case d
d. The ramp is curved.
Use the work-energy theorem to rank the final speeds of the block on the ramps (a-d), assuming
the block is launched with the same initial speed in each case. If the final speeds are the same in
any of the cases, state that explicitly. Explain.
Transcribed Image Text:4. A block is launched up a frictionless ramp, as shown,
with initial speed v,. The block travels up the ramp
and continues across the level section.
a. List the forces exerted on the block after it has
been launched, as it moves up the ramp.
Two forces are acting on the block; gravitational force and a normal force.
Which forces, if any, do non-zero work on the block?
Work done by gravitational energy is non zero quantity.
Which forces, if any, do zero work on the block?
Work done by the typical force is at all times zero.
b. Write an expression for the net work done on the block from the bottom to the top of the
ramp. Express your answer in terms of one or more of the following quantities: the weight
mg of the block, the angle 0, and the height H of the ramp. Show your work.
W=1/2 m v^2c –mgh
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