A 34.3-kg child swings on a rope with a length of 6.11 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 start by considering the forces acting on the child at the bottom of the swing.
At the bottom of the swing, the child is moving in a circular path. In circular motion, there is a centripetal force that keeps the object moving in a curved path.
The tension in the rope provides the centripetal force needed to keep the child moving in a circle. So, we can equate the tension in the rope with the centripetal force.
The formula for centripetal force is:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the child (34.3 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, 6.11 m / 2 = 3.055 m)
Now, let's plug in the values and calculate the tension:
F = (34.3 kg * (4.2 m/s)^2) / 3.055 m
Calculating this equation, we get:
F ≈ 196.890 N
Therefore, the tension in the rope is approximately 196.890 Newtons.