Question

7.10 q: the diagram at right shows a 5.0 - kilogram bucket of water being swung in a horizontal circle of 0.70 - meter radius at a constant speed of 2.0 meters per second. the magnitude of the centripetal force on the bucket of water is approximately (a) 5.7 n (b) 14 n (c) 29 n (d) 200 n 7.11 q: a 1.0 × 10³ - kilogram car travels at a constant speed of 20 meters per second around a horizontal circular track. which diagram correctly represents the direction of the car’s velocity (v) and the direction of the centripetal force (f_c) acting on the car at one particular moment?

Explanation:

Step1: Recall centripetal force formula

The formula for centripetal force is \(F_{c}=\frac{mv^{2}}{r}\), where \(m\) is mass, \(v\) is speed, and \(r\) is radius.

Step2: Substitute given values

Given \(m = 5.0\space kg\), \(v=2.0\space m/s\), \(r = 0.70\space m\).
Substitute into the formula: \(F_{c}=\frac{5.0\times(2.0)^{2}}{0.70}=\frac{5.0\times4.0}{0.70}=\frac{20}{0.70}\approx28.57\space N\)

Answer:

C. \(29\space N\)