Before practicing his routine on the rings, a 67 kg gymnast hangs motionless, with one hand grasping each ring and his feet touching the grounnd. Both arms make an angle of 24 degrees with the vertical.(a) If the force exerted by the rings on each arm has a magnitude of 290 N, what is the magnitude of the force exered by the floor on his feet? (b) If the angle his arms make with the vertical had been greater that 24 degrees, would the force exerted by the value found in part (a). explain.

Question

Before practicing his routine on the rings, a 67 kg gymnast hangs motionless, with one hand grasping each ring and his feet touching the grounnd. Both arms make an angle of 24 degrees with the vertical.(a) If the force exerted by the rings on each arm has a magnitude of 290 N, what is the magnitude of the force exered by the floor on his feet? (b) If the angle his arms make with the vertical had been greater that 24 degrees, would the force exerted by the value found in part (a). explain.

Answer 1

To solve this problem, we will use the concept of forces and equilibrium. In this scenario, the gymnast is in a state of equilibrium, which means that the net force acting on him is zero.

(a) To find the magnitude of the force exerted by the floor on his feet, we need to first resolve the forces acting on the gymnast.

Let's consider the forces acting on one of the arms. We have the force exerted by the rings (290 N) acting upward and at an angle of 24 degrees with the vertical. We need to find the vertical component of this force, which will be equal to the force exerted by the floor on his feet.

The vertical component of a force can be calculated using trigonometry. In this case, we can use the sine function because the angle is between the vertical direction and the force. The equation is:

Vertical force = Magnitude of the force * sin(angle)
Vertical force = 290 N * sin(24 degrees)

Calculating this, we find:
Vertical force = 290 N * 0.4067
Vertical force ≈ 117.868 N

Therefore, the magnitude of the force exerted by the floor on his feet is approximately 117.868 N.

(b) If the angle between his arms and the vertical had been greater than 24 degrees, the force exerted by the floor on his feet would be larger. This happens because as the angle increases, the vertical component of the force exerted by the rings also increases. Thus, the vertical force acting on his feet would be greater if the angle increased, resulting in a larger force exerted by the floor on his feet.

If you want to explore this further, you can try varying the angle and calculating the resulting forces using the same methodology explained above.