Question

A large crate is suspended from the end of a vertical rope. Is the tension in the rope greater when the crate is at rest or when it is moving upward at constant speed? If the crate is traveling upward, is the tension in the rope greater when the crate is speeding up or when it is slowing down? In each case, explain in terms of Newton’s laws of motion.

Answer 1

Part a)

the tension force is equal to the weight of the crate

Part b)

tension force is more than the weight of the crate while accelerating upwards

tension force is less than the weight of crate if it is accelerating downwards

Step-by-step explanation:

Part a)

When large crate is suspended at rest or moving with uniform speed then it is given as

`F_t - mg = ma`

here since speed is constant or it is at rest

so we will have

`a = 0`

`F_t = mg`

so the tension force is equal to the weight of the crate

Part b)

Now let say the crate is accelerating upwards

now we can say

`F_t - mg = ma`

`F_t = mg + ma`

so tension force is more than the weight of the crate

Now if the crate is accelerating downwards

`F_t - mg = -ma`

`F_t = mg - ma`

so tension force is less than the weight of crate if it is accelerating downwards