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14P (a)

Expert-verifiedFound in: Page 237

Book edition
9th Edition

Author(s)
Raymond A. Serway, John W. Jewett

Pages
1624 pages

ISBN
9781133947271

A crate of mass is pulled up a rough incline with an initial speed of . The pulling force is parallel to the incline, which makes an angle of with the horizontal. The coefficient of kinetic friction is , and the crate is pulled . (a) How much work is done by the gravitational force on the crate? (b) Determine the increase in internal energy of the crate–incline system owing to friction. (c) How much work is done by the force on the crate? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled?

(a) The work done by the gravitational force on the crate is .

The mass of the crate is m=10kg.

The initial speed of the crate is u=1.50$\frac{m}{s}$

The pulling force parallel to the incline is, F=100N.

The angle made by the pulling force with the horizontal is, $\theta =20$

The coefficient of kinetic friction is,${\mu}_{k}=0.400$

The distance the crate is pulled is, x=5.00m

The mechanical energy of a body is the combination of the change in the ‘The free-body diagram of the crate–incline system is given by,

Here, is the normal reaction force, and is the frictional force acting on the crate.

The formula for the work done by the gravitational force on the crate is given by,

${W}_{g}=mgx\mathrm{cos}(90+\theta )$

Substitute the values and solve as:

The negative sign indicates that the work is done against the gravity.

Hence, the work done by the gravitational force on the crate is 167.6J.

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