Question

A 4 kg mass is moving in a circular path of radius 2.5 m with a constant speed of 5 m/sec.
The centripetal force on the mass is
a ) 20 N. b ) 25 N. c ) 40 N. d ) 45 N. e ) 35 N.

Answer 1

Answer on Question #41029, Physics, Mechanics

A 4 kg mass is moving in a circular path of radius 2.5 m with a constant speed of 5 m/sec. The centripetal force on the mass is

a) 20 N. b) 25 N. c) 40 N. d) 45 N. e) 35 N.

Solution:

Given:

$$\begin{array}{l} m = 4 \, kg, \\ r = 2.5 \, m, \\ v = 5 \, m/s, \\ F_{\text{centripetal}} = ? \\ \end{array}$$

Any motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force which means "center seeking" force. The force has the magnitude

$$F_{\text{centripetal}} = m \frac{v^2}{r}$$

Thus,

$$F_{\text{centripetal}} = 4 \cdot \frac{5^2}{2.5} = 40 \, N$$

Answer. c) 40 N.