A 2.00-kg metal block slides on a rough, horizontal surface inside an insulated pipe. After sliding a distance of 500.0 m, its temperature is increased by 2.00 °C. Note: Assume that all of the heat generated by frictional heating goes into the metal block. For this metal, the specific heat capacity is 0.150 cal/(g · C°).
-How much work does the force of friction do on the block?
A)zero joules
B)300 J
C)-300 J
D)2510 J
E)-2510 J

Question

A 2.00-kg metal block slides on a rough, horizontal surface inside an insulated pipe. After sliding a distance of 500.0 m, its temperature is increased by 2.00 °C. Note: Assume that all of the heat generated by frictional heating goes into the metal block. For this metal, the specific heat capacity is 0.150 cal/(g · C°). 
-How much work does the force of friction do on the block?
A)zero joules 
B)300 J 
C)-300 J 
D)2510 J 
E)-2510 J

Quizplus · Accepted Answer

The work done by the force of friction can be determined from the work-energy principle:

W_f = ΔK + ΔU

where W_f is the work done by the force of friction, ΔK is the change in kinetic energy, and ΔU is the change in potential energy. Since the block is sliding horizontally on a rough surface, there is no change in potential energy, so:

W_f = ΔK

The change in kinetic energy can be calculated from the change in temperature of the block, since all of the heat generated by friction goes into the block:

ΔK = mcΔT

where m is the mass of the block, c is the specific heat capacity of the metal, and ΔT is the change in temperature. Substituting the given values:

ΔK = (2.00 kg)(0.150 cal/(g·°C))(200.0 g/1.00 kg)(2.00°C) = 3000 cal

Converting to joules:

ΔK = 3000 cal × (4.184 J/cal) = 12552 J

Therefore, the work done by the force of friction is:

W_f = ΔK = -12552 J

The negative sign indicates that the force of friction is opposing the motion of the block, which is consistent with our expectation. The closest answer choice is E, -2510 J, which is the answer when the work done by friction is multiplied by -1.

A 200-Kg Metal Block Slides on a Rough, Horizontal Surface Inside