The tension in the rope when the gymnast climbs it at constant speed is 641.9 N.
Given:
Mass of gymnast, m = 65.5 kg
The speed 'v' of gymnast is constant
Solution:
Consider the free-body diagram of the system as shown below.
Balancing forces along the vertical axis we get:
ΣFy = 0
Thus, we get:
F = ma - (1)
where, m is mass of gymnast
a is acceleration of gymnast (a = 0m/s², as the speed is constant)
Also,
F = T - mg -(2)
where, T is tension in the rope
g is acceleration due to gravity
Equating (1) & (2), we get:
ma = T - mg
Re-arranging the equation, we get:
T = m(a+g)
Applying values in above equation we get:
T = (65.5 kg)(0 m/s²+9.8 m/s²)
T = 641.9 N
Therefore, the tension in the rope when the gymnast climbs it at constant speed is 641.9 N.
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