A small body of mass m is located on a horizontal plane at …

Physics Work, Energy, Power and Collision Mix MCQ (Single Correct)

A small body of mass m is located on a horizontal plane at the point O. The body acquires a horizontal velocity v 0 . Find:

the mean power developed by the friction force during the whole time of motion, if the friction coefficient k = 0.27, m = 1.0 kg, and v 0 = 1.5 m/s;

the maximum instantaneous power developed by the friction force, if the friction coefficient varies as k = αx, where α is a constant, and x is the distance from the point O.

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Let the body m acquire the horizontal velocity along -axis at the point O.

Velocity of the body t second after the begining of the motion,

… ..(1)

Instantaneous power

From Eq. (1), the time of motion
Hence sought average power during the time of motion

From

To find , let us integrate the above equation

… .(1)

Now,

… ..(2)

For maximum power,
which yields
Putting this value of , in Eq. (2) we get,

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