An object of mass 8 kg is at the top of a hill that has three segments: (i) An i

Question

An object of mass 8 kg is at the top of a hill that has three segments:

(i) An incline of length 21 m that starts from the ground and is at an angle of pi divided by 3 above the horizontal

(ii) An incline of length 3 m that is horizontal and is connected to (i)

(iii) An incline of length 22 m that is at an angle of pi divided by 4 above the horizontal and is connected to (ii)

The object experiences a force of gravity similar to that of Earth's surface. Assume that the object and the hill have a constant coefficient of friction of 0.1 and it does not stop at any point.

If all energy lost to friction is converted to heat, determine the change in temperature of the object if the thermal energy is distributed uniformly over the entire object and the object has a heat capacity of 375 fraction numerator J over denominator k g degree C end fraction Report your answer in degrees Celsius.

Explanation / Answer

friction energy loss =heat energy = 0.1 x 8 x 9.8 (21cos(pi/3) + 3 + 22cos(pi/4)) = 227.8 J

now mc(dT) = 227.8

=> dT = 227.8/(8 x 375) = 0.075934 oC

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