an 85.0kg mountaineer remains in equilibrium while climbing a vertical cliff. the tension force in the supporting rope is 745 N. Find the magnitude of the reaction force F, which the cliff exerts on the mountaineer's feet.
85*9.81 - 745 Newtons
To solve this problem, we need to consider the forces acting on the mountaineer.
1. The gravitational force (weight) acting downward, which can be calculated using the formula: weight = mass * gravity.
In this case, weight = 85.0 kg * 9.8 m/s^2 (acceleration due to gravity) = 833 N.
2. The tension force in the supporting rope acting upward, which is given as 745 N.
Now, let's draw a free body diagram to visualize the forces acting on the mountaineer:
|
|
Tension - | \ / -
| \ /
| [mountaineer]
| / \
| / \
| / \
| /
In equilibrium, the sum of the forces in the vertical direction must be zero. Since the mountaineer is not accelerating vertically, the force exerted by the cliff on the mountaineer's feet (reaction force) must balance out the downward forces.
So, the equation for equilibrium in the vertical direction is:
F - Weight - Tension = 0
Substituting the given values, we have:
F - 833 N - 745 N = 0
Simplifying the equation:
F = 833 N + 745 N
F = 1578 N
Therefore, the magnitude of the reaction force (F) that the cliff exerts on the mountaineer's feet is 1578 N.