Question

1. a pendulum 1.00 m long and with a 1.20 kg bob is swinging with a maximum speed of 2.50 m/s. calculate the total force exerted by the string on the swinging mass when the mass is at the bottom of its swing.

Explanation:

Step1: Analyze the forces acting on the pendulum bob

At the bottom of the swing, the forces acting on the pendulum bob are the tension \(T\) in the string (upward) and the force of gravity \(mg\) (downward). The net force provides the centripetal force \(F_c=\frac{mv^{2}}{r}\). Using Newton's second law \(F_{net}=T - mg=\frac{mv^{2}}{r}\), so \(T = mg+\frac{mv^{2}}{r}\).

Step2: Substitute the given values

We are given \(m = 1.20\space kg\), \(v=2.50\space m/s\), \(r = L=1.00\space m\), and \(g = 9.8\space m/s^{2}\).
Substitute into the formula \(T=(1.20\times9.8)+\frac{1.20\times(2.50)^{2}}{1.00}\).
First calculate \(1.20\times9.8 = 11.76\).
Then calculate \(\frac{1.20\times(2.50)^{2}}{1.00}=\frac{1.20\times6.25}{1.00}=7.5\).

Step3: Calculate the value of \(T\)

\(T=11.76 + 7.5\).

Answer:

\(T = 19.26\space N\)