Bob is working in his barn one day. He has a 25 kg hay bale suspended from the b
ID: 1474220 • Letter: B
Question
Bob is working in his barn one day. He has a 25 kg hay bale suspended from the barn's rafters on a 2.44 meter long rope. Bob pulls on another rope horizontally until the rope holding the hay bale makes an angle of 20 degrees with respect to the vertical.
a) What force does Bob have to exert on the rope to hold the hay bale in this position?
b) The rope slips out of Bob's hands. The hay bale starts to swing. How long does it take for the hay bale to swing to the farthest distance from where it started (the farthest distance across the barn)?
c) Bob runs to catch the hay bale. He tries to catch it at the bottom of the swing as it swings back towards him. How fast is the hay bale moving when it hits Bob?
Explanation / Answer
In vertical,
Tcos20 - mg = 0
T = (25 x 9.81) / cos20 = 261 N
In horizontal,
F = Tsin20 = 261sin20 = 89.26 N ........Ans
b) time period of oscillation T = 2pi sqrt(L/g)
T = 2pi sqrt(2.44 / 9.81) = 3.13 sec
time taken to reach farthest point = T/2 = 1.57 sec
c) height of initial position from lowest point h = L - Lcos20 = 0.147 m
using energy conservation
mv^2 /2 = mgh
v^2 = 2 x 9.18 x 0.147
v = 1.70 m/s