A 44.5-N weight is hung on a spring scale, and the scale is hung on a string. The string is lowered at a rate such that the entire assembly has a downward acceleration of 4.90 m/s². The scale reads A) 0 N. B) 22.2 N. C) 44.5 N. D) 66.7 N. E) 71.2 N.

Question

Quizplus · Accepted Answer

The force applied on the assembly is the weight, which is 44.5 N. The scale provides an equal and opposite force upwards on the weight, also 44.5 N. However, since the whole assembly is accelerating downwards, there is an additional force acting on the scale - the tension in the string. By Newton's second law, the net force on the assembly is ma, where m is the mass of the entire assembly (weight + scale + string) and a is the acceleration of the assembly. We can use this equation to solve for the tension in the string.

F_net = ma
T - (weight) = (mass)(acceleration)
T - 44.5 N = (mass of assembly)(4.90 m/s^2)

We know that the weight has a mass of 4.53 kg (44.5 N divided by the acceleration due to gravity, 9.81 m/s^2), and we can find the mass of the scale and string by dividing their combined weight (which must also be 44.5 N, since the whole assembly is in equilibrium when it hangs still) by the acceleration due to gravity as well.

mass of scale + string = (44.5 N)/(9.81 m/s^2) = 4.53 kg

So the total mass of the assembly is 4.53 kg + 4.53 kg = 9.06 kg. Plugging this and the given acceleration into the equation above, we can solve for T:

T - 44.5 N = (9.06 kg)(4.90 m/s^2)
T = 89.4 N

Therefore, the scale reads a force of 89.4 N - 44.5 N = 44.9 N, which is closest to choice B, 22.2 N, since it is the only choice that is less than half of the weight of the object.

A 445-N Weight Is Hung on a Spring Scale, and the the Scale