A 31.5-kg child swings on a rope with a length of 6.26 m that is hanging from a tree. At the bottom of the swing, the child is moving at a speed of 4.2 m/s. What is the tension in the rope?
To find the tension in the rope, we can use the concept of centripetal force. The tension in the rope provides the centripetal force required to keep the child moving in a circular path.
The centripetal force can be calculated using the equation:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the child (31.5 kg)
v is the velocity of the child (4.2 m/s)
r is the radius of the circular path (half the length of the rope)
Since the length of the rope is given, we can calculate the radius by dividing the length by 2:
r = 6.26 m / 2 = 3.13 m
Now we can substitute the values into the equation to find the centripetal force:
F = (31.5 kg * (4.2 m/s)^2) / 3.13 m
F = (31.5 kg * 17.64 m^2/s^2) / 3.13 m
F ≈ 177.26 N
Therefore, the tension in the rope is approximately 177.26 Newtons.