Question

A wrecking ball utilized to knock down structures has a mass of m=1490 kg and is hanging from a cable of length L= 19 m. It reaches a maximum speed of v= 18 m/s while traveling in a circular arc in the direction of the structure.

a) What is the minimum tension in N that the cable must be able to support without breaking? Assume the cable is massless.

b) If the cable can only support a tension of 10,000 N what is the highest mass the ball can have in kg?

Answer 1

Given.mass =1490kg and length=19m

Maximum speed =18m/s

Now

When the ball is at the lowest point then tension will be maximum of the swing so minimum tension the cable must be able to support.

tension at minimum point is:
T = m×(Ac + g)
where
m = mass = 1490 kg
g = acceleration by gravity = 9.8 m/s²
Ac = centripetal acceleration

The centripetal acceleration can be found by
Ac = V²/R
where
V= speed = 18m/s
R = radius of the swing = 19 m=length of rod

Now
T = m×(v²/R + g)
T = 1490×(18²/19 + 9.8)
T = 40025.32 N

As given in question rod can withstand only 10000 N, then the maximum mass is:
10000 = m×(18²/19 + 9.8)
m = 37.23 kg

So maximum mass = 37.23 kg

Hope you got.rate please