Question

1. the cement bag shown in the figure has a mass of 50 kg and the small pulley has a mass of 2 kg. if the cement bag is pulled upwards with an acceleration of 2 m/s², find the force f pulling the rope.

Explanation:

Step1: Analyze the forces acting on the system

The total mass being lifted is \(m = 50 + 2=52\space kg\). The force due to gravity is \(F_g=mg\), where \(g = 10\space m/s^2\). The net force \(F_{net}\) causing the acceleration \(a = 2\space m/s^2\) is \(F_{net}=ma\).

Step2: Use the pulley - force relationship

For a pulley system, if the force pulling the rope is \(F\), and considering the tension in the rope. The total force acting on the system (cement bag + small pulley) is \(3F\) (because of the way the rope is arranged around the pulleys). According to Newton's second law \(F_{net}=3F-(m)g\) and \(F_{net}=ma\). So, \(3F= m(a + g)\).
Substitute \(m = 52\space kg\), \(a=2\space m/s^2\) and \(g = 10\space m/s^2\) into the equation \(3F=52\times(2 + 10)\).

$$3F=52\times12$$

$$F=\frac{52\times12}{3}$$

$$F = 208\space N$$

Answer:

\(208\space N\)