   Chapter 4, Problem 85AP

Chapter
Section
Textbook Problem

Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in Figure P4.85, where m1 = 10.0 kg and m2 = 20.0 kg. A force of 50.0 N is applied to the 20.0-kg box. (a) Determine the acceleration of each box and the tension in the string. (b) Repeat the problem for the case where the coefficient of kinetic friction between each box and the surface is 0.10. Figure P4.85

(a)

To determine
The acceleration of the boxes and tension in the string.

Explanation

Given info: The masses of the blocks are m1 =10.0 kg and m2 =20.0 kg. Applied force is 50.0 N.

The free body diagram is given below.

• N1 and N2 are the normal forces.
• m1 and m2 are the masses of the blocks.
• g is the acceleration due to gravity.
• f1 and f2 are the friction forces.
• F is the applied force.

From the diagram,

Tf1=m1a (I)

N1=m1g (II)

FTf2=m2a (III)

N2=m2g (IV)

The formula for the friction forces is,

f1=μN1 (V)

f2=μN2 (VI)

• μ is the co-efficient of friction.

Substitute Equations (II) and (IV) in (V) and (VI) respectively.

f1=μm1g

f2=μm2g

Substitute the above equations in (I) and (III) respectively.

Tμm1g=m1a (VII)

FTμm2g=m2a (VIII)

Add Equation (VII) and (VIII) and re-arrange to get a.

a=Fm1+m2μg

For a frictionless surface, μ=0

(b)

To determine
The acceleration of the boxes and tension in the string.

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