Question

1. an object undergoing uniform circular motion has a centripetal force of 20 n and a mass of 5 kg.

a. what is the centripetal acceleration of the object?
b. if the objects path has a radius of 2 meters, what must be the tangential velocity of the object?

Explanation:

Step1: Use Newton's second law for centripetal force

Newton's second law \(F = ma\). For centripetal force \(F_c=ma_c\), where \(F_c = 20\space N\) and \(m = 5\space kg\). We solve for \(a_c\):

$$a_c=\frac{F_c}{m}$$

Substitute \(F_c = 20\space N\) and \(m = 5\space kg\) into the formula:

$$a_c=\frac{20}{5}=4\space m/s^{2}$$

Step2: Use the centripetal - acceleration formula \(a_c=\frac{v^{2}}{r}\)

We know \(a_c = 4\space m/s^{2}\) and \(r = 2\space m\). From \(a_c=\frac{v^{2}}{r}\), we can solve for \(v\).
First, rewrite the formula for \(v\): \(v=\sqrt{a_cr}\)
Substitute \(a_c = 4\space m/s^{2}\) and \(r = 2\space m\) into the formula:

$$v=\sqrt{4\times2}=\sqrt{8}=2\sqrt{2}\approx 2.83\space m/s$$

Answer:

a. The centripetal acceleration of the object is \(4\space m/s^{2}\).
b. The tangential velocity of the object is approximately \(2.83\space m/s\).