Question

If you used an ideal pulley of the type shown inFigure\({\rm{9}}{\rm{.26}}\)(a) to support a car engine of mass \({\rm{115}}\;{\rm{kg}}\), (a) What would be the tension in the rope? (b) What force must the ceiling supply, assuming you pull straight down on the rope? Neglect the pulley system’s mass.

Short answer

The tension in the rope is

1. \({\rm{563}}{\rm{.5}}\;{\rm{N}}\).
2. The ceiling force is \({\rm{1690}}{\rm{.5}}\;{\rm{N}}\).

Step-by-step solution

Force

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

Diagram

The diagram of the pulley system is shown below:

Calculation of the tension

(a)

For equilibrium, the upward force will be balanced by the downward weight. So,

\(\begin{align}mg &= 2T\\T &= \frac{{mg}}{2}\\ &= \frac{{115 \times 9.8}}{2}\\ &= 563.5\;N\end{align}\)

Hence, the tension is \({\rm{563}}{\rm{.5}}\;{\rm{N}}\).

Calculation of the ceiling force

(b)

Let, the ceiling force be\({{\rm{F}}_{\rm{c}}}\).

The pulley is used to support a car engine and the mass of the puller is negligible. So,

\(\begin{align}{F_c} &= 3T\\ &= 3 \times 563.5\\ &= 1690.5\;N\end{align}\)

Hence, the force is \({\rm{1690}}{\rm{.5}}\;{\rm{N}}\).