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?
(A) 0
(B) 0.5 g
(C) g
(D) 1.5 g
(E) 2.5 g

Answer 1

Answer:

(B) 0.5 g

Explanation:

Newton's second law says ∑  F i = m a .

the rate of change in momentum of a body is proportional to the force applied on the body.

f∝ma

f=kma

were k is constant and equal to 1

The centripetal acceleration is an acceleration.

the tension on the swing and object weight goes to the left hand side while the centripetal acceleration goes to the right handside

At the bottom of the swing, ΣF = FT – mg = mac;

notice that the tension in the swing is 1.5 times the weight of the object

we can write

1.5mg – mg = mac,

0.5mg = mac

0.5 g=ac

Answer 2

Answer:

Option B: 0.5g

Explanation:

It is established by Newtons second Law that Force = mass x acceleration.

Therefore, the notation below explains the relationship between Force, Tension and Weight at the bottom of the swing of a simple pendulum as cited in the question.

F = T - mg = mass x centripetal acceleration

where T represents Tension, and mg represents weight

Therefore,

Force = 6 newtons - 4 newtons = mass x acceleration

Our result becomes, 2 newtons = 4 newtons x acceleration ( Recall our mass is equal to 4 newtons)

Let our centripetal acceleration be represented by a,

2N = 4N x a

This gives us a = 2N/4N (by making "a" the subject of the formula)

Final answer is 0.5g or 1/2g.

Please note:

At the top, the relationship becomes : F = Tension(force) + Weight(mg) = (mass x velocity^2)/R.