A 5.40 kg block is set intomotion up an inclined plane with an initial speed of

Question

A 5.40 kg block is set intomotion up an inclined plane with an initial speed ofv0 = 8.10 m/s. Theblock comes to rest after traveling 3.00 m along the plane, whichis inclined at an angle of 30.0° to the horizontal. (a) For this motion, determine the change inthe block's kinetic energy.
J

(b) For this motion, determine the change in potential energy ofthe block-Earth system.
J

(c) Determine the frictional force exerted on the block (assumed tobe constant).
N

(d) What is the coefficient of kinetic friction?

A 5.40 kg block is set intomotion up an inclined plane with an initial speed ofv0 = 8.10 m/s. Theblock comes to rest after traveling 3.00 m along the plane, whichis inclined at an angle of 30.0° to the horizontal. (a) For this motion, determine the change inthe block's kinetic energy.
J

(b) For this motion, determine the change in potential energy ofthe block-Earth system.
J

(c) Determine the frictional force exerted on the block (assumed tobe constant).
N

(d) What is the coefficient of kinetic friction?

(a) For this motion, determine the change inthe block's kinetic energy.
J

(b) For this motion, determine the change in potential energy ofthe block-Earth system.
J

(c) Determine the frictional force exerted on the block (assumed tobe constant).
N

(d) What is the coefficient of kinetic friction?

Explanation / Answer

(a) Change in KE =   final KE - initial KE =   0 - (1/2) mv2 = .               =    - (1/2) * 5.40 *8.102     =   - 177.15 Joules . (b) Change in PE = mgh = 5.40 *9.80 * 3.00sin30 =    79.38Joules . (c)   total work by friction = total change in energy .              -friction force * distance = change inKE + change in PE .                -friction force * 3.00 = -177.15 + 79.38 .                friction force =    32.59 Newtons         (the answershould be positive, but if not try negative) . (d)    friction force = coeff *normal force .          32.59 = coeff * mgcos .          32.59 = coeff * 5.40 * 9.80 * cos30 .            coeff =    0.711

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