A child weighing 150 newtons is sitting in a swing. The swing is
supported by two ropes, one on each side. What is the tension in
one of the ropes?
half the weight is supported by each rope, right?
150/2 75N each rope
To find the tension in one of the ropes supporting the swing, we need to consider the forces acting on the swing.
In this case, we have the weight of the child pulling downward, which is equal to 150 newtons. This force acts at the center of the swing.
Since the swing is supported by two ropes, there is a tension force in each rope. These tension forces act upwards and balance the weight of the child.
Since the child is at rest (not accelerating vertically), the sum of the upward tension forces must equal the weight of the child.
So, the tension in one of the ropes would be half of the child's weight:
Tension in one rope = Weight of child / 2 = 150 newtons / 2 = 75 newtons.
Therefore, the tension in one of the ropes supporting the swing is 75 newtons.
To find the tension in one of the ropes supporting the swing, we need to consider the forces acting on the swing.
1. Start by drawing a free-body diagram. This will help visualize the forces involved. Draw a dot to represent the swing, and draw arrows to represent the forces acting on it.
2. In this case, we have three forces acting on the swing: the weight of the child (150 newtons), and the tensions in the two ropes (Tension1 and Tension2).
3. Since the swing is at rest, the net force acting on it must be zero. This means that the upward forces must balance out the downward force. Therefore, the sum of the vertical forces should be equal to zero.
4. In this scenario, the only upward force is the tension in the ropes, while the downward force is the weight of the child. So we can set up an equation:
Tension1 + Tension2 - Weight = 0
Rearranging the equation, we can solve for Tension1:
Tension1 = Weight - Tension2
5. Substitute the given values into the equation. In this case, the weight of the child is 150 newtons:
Tension1 = 150 N - Tension2
6. Since the swing is symmetrical, the tension in both ropes is equal. Therefore, we can rewrite the equation as:
Tension1 = 150 N - Tension1
7. Solve the equation for Tension1:
2 * Tension1 = 150 N
Tension1 = 150 N / 2
Tension1 = 75 newtons
So, the tension in one of the ropes supporting the swing is 75 newtons.