Question

An aluminum rod is designed to break when it is under a tension of 600 N. One end of the rod is connected to a motor and a 12-kg spherical object is attached to the other end. When the motor is turned on, the object moves in a horizontal circle with a radius of 5.78 m. If the speed of the motor is continuously increased, at what speed will the rod break

Answer 1

Answer:

17 m/s

Explanation:

Given:

Tension = 600 N

Mass of object, M= 12 kg

Radius, r = 5.78 m

Required:

Find the speed the rod will break

Here, the motor is continuously increased. To find the speed the rod will break (speed of centripetal force), we have:

Tension = Centripetal force

Where centripetal force = $\frac{mv^2}{r}$

Therefore,

$T = \frac{mv^2}{r}$

Make v subject of the formula:

$v = \sqrt{\frac{T*r}{m}}$

$= \sqrt{\frac{600*5.78}{12}}$

$= \sqrt{\frac{3468}{12}$

$= \sqrt{289}$

$= 17 m/s$

Speed the rod will break is 17 m/s.