Question.1 The figure shows two blocks, A and B, that are initially at rest at a

Question

Question.1

The figure shows two blocks, A and B, that are initially at rest at a height h above the ground. At time t = 0, block A is dropped and falls without friction; block B is allowed to slide down a frictionless ramp.

Which of the blocks has the larger speed when it reaches the ground?

1)Block A

2)Block B

3)Both blocks have the same speed.

4)Not enough information to decide.

Question.2

If the ramp in the previous question is NOT frictionless, which of the blocks has the larger speed?

1)Block A

2)Block B

3)Both blocks have the same speed.

4)Not enough information to decide.

Explanation / Answer

Question 1:

Because there is no friction we can assume energy conservation applies:
Eo=Ef (The initial mechanical energy equals the final mechanical energy)

Eo=mgho+(1/2)mvo2 (The initial mechanical energy is the sum of initial potential and initial kinetic energy)

In the initial state, both blocks start from rest so the kinetic energy term vanishes

Eo=mgh

Next we look at the final state:

Ef=mghf+(1/2)mvf2

In the final state,both blocks are at a height of 0 so the potential energy term vanishes:

Ef=(1/2)mvf2

We dont know what vf is but thats ok energy conservation will tell us:

Eo=Ef

mgh=(1/2)mvf2

vf=Sqrt(2gh)

So both blocks will have the same speed

Intuitively this is difficult to accept becuase the first block gets to fall at g while the second doesn't but consider the fact that the second block makes up for this by having an increased velocity component in the x direction which is the result of the normal force that the plane exerts on the block

Question 2:

Because there is now friction some energy is lost to heat so we can no longer use energy conservation.

Block A will have the larger speed because block B is limited in both the y direction (it doesn't get to free fall at g) and the x direction (friction is acting against it)

Hope this helps :)

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