A block of material of mass m and specific heat c falls from height h and reaches speed v just before striking the ground. Its temperature is measured immediately after it strikes the ground. If we ignore any change in temperature owing to interaction with the air, the change in temperature of the block of material is
A) .
B) .
C) .
D) All of the answers above are correct.
E) Only (a) and (b) above are correct.

Question

A block of material of mass m and specific heat c falls from height h and reaches speed v just before striking the ground. Its temperature is measured immediately after it strikes the ground. If we ignore any change in temperature owing to interaction with the air, the change in temperature of the block of material is
A) . 
B) . 
C) . 
D) All of the answers above are correct. 
E) Only (a) and (b) above are correct.

Quizplus · Accepted Answer

The change in temperature of the block of material can be calculated using the equation:

ΔT = (mv^2)/(mc)

where m is mass, v is speed, c is specific heat, and ΔT is the change in temperature.

Since the block falls from height h, we can assume that all of its potential energy is converted to kinetic energy just before it strikes the ground. Therefore, the speed of the block can be calculated using the equation:

v = (2gh)^0.5

where g is the acceleration due to gravity.

Substituting this into the equation for ΔT, we get:

ΔT = m(2gh)^0.5/(mc)

Simplifying this expression, we get:

ΔT = 2gh/c^2

This means that ΔT depends only on the height the block falls from and the specific heat of the material. Therefore, choices (a) and (b) are correct, but choice (c) is not. Since all of the answers above contain either (a) or (b), the correct answer is E: Only (a) and (b) above are correct.

A Block of Material of Mass M and Specific Heat