Question

An object weighing 4 newtons swings on the end of a string as a simple pendulum. At the bottom of the swing, the tension in the string is 6 newtons. What is the magnitude of the centripetal acceleration of the object at the bottom of the swing?

Answer 1

4.9 m/s^2

Step-by-step explanation:

weight, mg = 4 N

Tension, T = 6 N

Let a be the centripetal acceleration.

let m be the mass, m = 4 / 9.8 = 0.41 kg

At the bottom, the tension is given by

T - mg = ma

6 - 4 = ma

ma = 2

0.41 x a = 2

a = 4.9 m/s^2

Thus, the centripetal acceleration is 4.9 m/s^2.

Answer 2

0.5g or 4.905 m/s²

Step-by-step explanation:

`F_T` = Tension =
`6\ N\ or (6)/(4)mg`

`a_c` = Centripetal acceleration

g = Acceleration due to gravity = 9.81 m/s²

In this system the forces are conserved

`\Sigma F=F_T-mg=ma_c\\\Rightarrow (6)/(4)mg-mg=ma_c\\\Rightarrow a_c=1.5g-g\\\Rightarrow a_c=0.5g\\\Rightarrow a_c=0.5* 9.81\\\Rightarrow a_c=4.905\ m/s^2`

The magnitude of the centripetal acceleration of the object at the bottom of the swing is 0.5g or 4.905 m/s²