A 50 kg uniform ladder, 5.0 m long, is placed against a smooth wall at a height of h = 3.7 m. The base of the ladder rests on a rough horizontal surface whose coefficient of static friction is 0.40. An 80 kg block is suspended from the top rung of the ladder, just at the wall. In the figure, the magnitude of the force exerted on the base of the ladder, due to contact with the rough horizontal surface is closest
density of an object with the mass 7kg and the volume 2.5L
To determine the magnitude of the force exerted on the base of the ladder, we need to consider the forces acting on the ladder system.
1. Weight of the ladder:
The weight of the ladder can be calculated using the formula: weight = mass × gravitational acceleration.
Weight of the ladder = 50 kg × 9.8 m/s² = 490 N.
2. Weight of the block:
The weight of the block can be calculated in the same way, using its mass and gravitational acceleration.
Weight of the block = 80 kg × 9.8 m/s² = 784 N.
3. Normal force exerted by the wall:
The normal force exerted by the wall is equal in magnitude and opposite in direction to the force exerted by the ladder on the wall. It can be calculated using the formula: normal force = weight of the block + weight of the ladder.
Normal force = 784 N + 490 N = 1274 N.
4. Friction force exerted by the rough horizontal surface:
The coefficient of static friction is given as 0.40. The maximum friction force that can be exerted is equal to the coefficient of static friction multiplied by the normal force.
Friction force = coefficient of static friction × normal force.
Friction force = 0.40 × 1274 N = 509.6 N.
Therefore, the magnitude of the force exerted on the base of the ladder, due to contact with the rough horizontal surface, is approximately 509.6 N.