Question

A 2-kg metal block slides on a rough horizontal surface inside an insulated box. After
sliding a distance of 500.0 m, its temperature increased by 2.00 0C. Assuming that all
heat generated by frictional heating goes into the metal block, and the metal has a
specific heat capacity of 0.150 cal/(g.0C), find:
(i) How much work (heat Q) does the force of friction does on the block?
(ii) What is the coefficient of kinetic friction between the block and the surface?

Answer 1

Answer on Question #40934, Physics, Mechanics | Kinematics | Dynamics

Question:

A 2-kg metal block slides on a rough horizontal surface inside an insulated box. After sliding a distance of 500.0 m, its temperature increased by 2.00 0C. Assuming that all heat generated by frictional heating goes into the metal block, and the metal has a specific heat capacity of 0.150 cal/(g.0C), find:

(i) How much work (heat Q) does the force of friction does on the block?

(ii) What is the coefficient of kinetic friction between the block and the surface?

Answer:

(i) The law of conservation of energy:

$$Q = A$$

where $Q$ is amount of heat, $A$ is work.

Amount of heat equals:

$$Q = c m \Delta t = 0.15 \frac{cal}{g{}^{\circ} \mathrm{C}} \cdot 2000 g \cdot 2{}^{\circ} \mathrm{C} = 600 \, \mathrm{cal} = 2512 \, J$$

(ii) Work equals:

$$A = F d$$

where $F$ force of friction, $d$ is distance.

Force of friction equals:

$$F = \mu m g$$

Therefore coefficient of kinetic friction equals:

$$\mu = \frac{A}{m g d} = 0.2561$$

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