A 1240-kg car pulls a 360-kg trailer. The car exerts a horizontal force of 3.6 ×

Question

A 1240-kg car pulls a 360-kg trailer. The car exerts a horizontal force of 3.6 × 103 N against the ground in order to accelerate.

Part A

What force does the car exert on the trailer? Assume an effective friction coefficient of 0.16 for the trailer.

Express your answer to two significant figures and include the appropriate units.

A 1240-kg car pulls a 360-kg trailer. The car exerts a horizontal force of 3.6 × 103 N against the ground in order to accelerate.

Part A

What force does the car exert on the trailer? Assume an effective friction coefficient of 0.16 for the trailer.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Refer below figure,

mg, trailer's weight acts down
Fn=normal force acts up
T= force of car acts forward (tension)
f= frictional force acts backward

mass of trailer = m=1240kg , mass of the car = M = 360kg

Apply Newton's second law in the vertical direction:
Fn - mg = 0
Fn = mg

Apply Newton's second law in the horizontal direction:
T - f = ma
T = ma + f
T = ma + µFn
T = ma + µmg
T = m(a + µg)

The car and the trailer move together because they are connected. Therefore, they will have the same acceleration. To determine the acceleration, apply Newton's second law to the combined system of the car and the trailer:
F = (m + M)a
a = F/(m + M)
F is the horizontal force that the ground exerts on the car, which is equal and opposite to the force that the car exerts on the ground.

T = m[F/(m + M) + µg] Plugging values,

T= 1240[3600/(1240+360)+0.15*9.8] = 4612.8 N

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