Question

A 0.80 kg object tied to the end of a 2.0 m string swings as a pendulum. At the lowest point of its swing, the object has a kinetic energy of 10 J. Determine the speed of the object at the instant when the string makes an angle of 50o with the vertical.

Answer 1

Answer:

3.32 m/s

Explanation:

From the law of conservation of energy, the sum of mechanical and kinetic energy should be equal to the 10 J given. Potential energy is given by mgh where m is mass, g is acceleration due to gravity and h is the height. For this case, $h= l(1-cos\theta)$ and l is string length, given as 2 m, \theta is given as 50 degrees. Kinetic energy is given by $0.5mv^{2}$ and it is this velocity that is unknown.

$10J=0.5\times 0.8kg\times v^{2}+ 0.8kg\times 9.81\times 2m(1-cos 50^{\circ})\\v\approx 3.32 m/s$