Question

An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1130 N. The coefficient of static friction between the box and the floor is 0.390. (a) What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?

Answer 1

Answer:

(a). if  $\theta$ = 0° , we can pull the greatest possible amount  of sand.

(b). The value of weight of sand and box = 2897.43 N

Explanation:

Maximum tension in the cable $T_{max}$ = 1130 N

The coefficient of static friction $\mu$ = 0.39

(a). Let the angle between the cable and the horizontal = $\theta$

From the free body diagram, T $\cos \theta$ = F ------ (1)

For maximum amount of force value of $\cos \theta$ must be maximum, it is only possible when $\theta$ = 0°

⇒ $\cos \theta$ = $\cos 0$° = 1

⇒ From equation (1)  we get

⇒T = F = 1130 N -------- ( 2 )

therefore if  $\theta$ = 0° , we can pull the greatest possible amount  of sand.

(b). From the free body diagram,

Force acting on the box F = $\mu$ $R_{N}$

Put the value of F from equation 2 we get,

⇒ 1130 = 0.39  $R_{N}$

⇒ $R_{N}$ = 2897.43 N --------- ( 3 )

From Free body diagram, Value of $R_{N}$ is equal to weight of the and and box.

⇒ $R_{N}$ = W

⇒ W = 2897.43 N

This is the value of weight of sand and box.