Question

A kid with 50kg runs and jump onto a tire swing with mass of 10kg. The tire and the kid rise 1.25m.

a. what is the kid's initial velocity? (must use conservation of momentum at least)

b. if the rope is 10 meters, what is the max tension? (draw a free body diagram)

c. What is the tension when the swing is at maximum height?

Answer 1

a)

using conservation of energy

0.5* (m1 +m2) v^2 = (m1 + m2) gh

v^2 = 2 * 9.8* 1.25

v = 4.95 m/s

using conservation of momentum

m1 u 1 = (m1 + m2) v

50 u1 = (50 +10) 4.95

u1 = 5.94 m/s

=======

b)

max tension

T = mv^2 /r + mg

T = 60* 4.95^2 / 10 + 60*9.8

T = 735 N

=====

c)

angle with vertical at max height

cos x = ( 10 - 1.25) / 10

x = 28.96

Tension at max height

T = mg cos x

T = 514.48 N

==========

Comment in case any doubt, will reply for sure.. Goodluck