A 0.2-kg aluminum plate,initially at 20°C,slides down a 10-m long surface,inclined at a 30° angle to the horizontal.The force of kinetic friction exactly balances the component of gravity down the plane so that the plate,once started,glides down at constant velocity.If 90% of the mechanical energy of the system is absorbed by the aluminum,what is its temperature increase at the bottom of the incline? (Specific heat for aluminum is 900 J/kg · °C. )

Question

Quizplus · Accepted Answer

We can start by finding the initial kinetic energy of the aluminum plate using conservation of energy:

K_initial = mgh = (0.2 kg)(9.81 m/s^2)(10 m sin 30°) = 9.81 J

Since the plate is gliding down at constant velocity, its final kinetic energy is also 9.81 J. Since 90% of the mechanical energy is absorbed by the aluminum, we can set up the following equation:

0.9(K_initial) = mcΔT

where c is the specific heat for aluminum and ΔT is the temperature increase. Solving for ΔT:

ΔT = 0.9(K_initial)/(mc) = [0.9(9.81 J)] / [(0.2 kg)(900 J/kg·°C)] = 0.05°C

Therefore, the temperature of the aluminum plate increases by 0.05°C at the bottom of the incline. The closest choice to this value is C, 0.05°C.

A 02-Kg Aluminum Plate,initially at 20°C,slides Down a 10-M Long Surface,inclined