Answer to Question #279721 in Physics for Abdo

Question

A simple pendulum has a mass of 0.250 kg and a length of 1.00 m. It

is displaced through an angle of 15.0° and then released. What are (a)

the maximum speed, (b) the maximum acceleration, and (c) the

maximum restoring force? What If? Solve this problem by using the

simple harmonic motion model for the motion of the pendulum, and

then solve the problem more precisely by using more general

principles.

Answer 1

(a) The speed:

$$v=\sqrt{2gL\cos\theta}=4.35\text{ m/s}.$$

(b) The acceleration:

$$a=v^2/r=4.35\text{ m/s}^2.$$

(c) The maximum restoring force:

$$F=m\bigg(g+\frac{v^2}g\bigg)=7.2\text{ N}.$$