A 0.200-kg aluminum plate,initially at 20°C,slides down a 13.0-m-long surface,inclined at a 25.0° 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

First, we need to find the initial mechanical energy of the system. Using conservation of energy, we have:

Initial mechanical energy = mgh = (0.200 kg)(9.81 m/s^2)(sin 25°)(13.0 m) = 24.1 J

Since 90% of this energy is absorbed by the aluminum plate, the plate gains an amount of thermal energy equal to 0.9 times the initial mechanical energy:

Thermal energy gained by plate = 0.9(24.1 J) = 21.7 J

To find the temperature increase, we divide the thermal energy gained by the specific heat of aluminum and the mass of the plate:

ΔT = (21.7 J)/(0.200 kg)(900 J/kg⋅°C) = 0.0538 °C

Therefore, the temperature of the aluminum plate increases by approximately 0.0538°C at the bottom of the incline. The correct answer is B.

A 0200-Kg Aluminum Plate,initially at 20°C,slides Down a 13