Question

a wrecking ball has a mass of 650 kg. it swings from a cable that is 21 m long. the centripetal force on the ball is 56 n. what is the tangential speed of the wrecking ball? 1.3 m/s 1.8 m/s 46 m/s 870 m/s

Explanation:

Step1: Recall the centripetal force formula

The centripetal force formula is \(F_{c}=\frac{mv^{2}}{r}\), where \(F_{c}\) is the centripetal force, \(m\) is the mass, \(v\) is the tangential speed, and \(r\) is the radius (length of the cable in this case).
We need to solve for \(v\). Rearranging the formula for \(v\) gives \(v = \sqrt{\frac{F_{c}r}{m}}\).

Step2: Substitute the given values

Given \(F_{c}=56\space N\), \(m = 650\space kg\), and \(r=21\space m\).
Substitute these values into the formula: \(v=\sqrt{\frac{56\times21}{650}}\).
First, calculate the numerator: \(56\times21 = 1176\).
Then, \(\frac{1176}{650}\approx1.81\).
Finally, \(v=\sqrt{1.81}\approx 1.3\space m/s\).

Answer:

1.3 m/s