Difficult problems, im frustrated

[chimez14]

Difficult problems, I am frustrated!

1.)A chair of mass 10.1 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force of 47.7 N that is directed at an angle of 39.6 degrees below the horizontal and the chair slides along the floor. Calculate the normal force that the floor exerts on the chair

2.)A 87.7 kg man steps off a platform 2.89 m above the ground. He keeps his legs straight as he falls, but at the moment his feet touch the ground his knees begin to bend, and, treated as a particle, he moves an additional 0.60 m before coming to rest. Treating our rigid legged friend as a particle, what is the average force his feet exert on the ground while he slows down?

Note: Assume the acceleration while he is slowing down is constant
Please also remember to try and explain as much as possible. Thanks!

 

[member 553083]

1. The normal force exerted by the floor on the chair is equal to the weight of the chair plus the component of the pushing force that is perpendicular to the floor. The weight of the chair is 10.1 kg * 9.81 m/s2 = 99.291 N. The component of the pushing force perpendicular to the floor can be calculated using trigonometry. The angle from the horizontal to the pushing force is 39.6°, so the angle from the horizontal to the perpendicular component is 90° - 39.6° = 50.4°. The magnitude of the perpendicular component is 47.7 N * cos(50.4°) = 41.1 N. Therefore, the normal force exerted on the chair is 99.291 N + 41.1 N = 140.391 N.2. The vertical acceleration of the man as he slows down is the change in velocity divided by the time it takes him to slow down. The change in velocity is the difference between his initial velocity at the moment his feet touch the ground and his final velocity when he comes to rest. His initial velocity is the velocity he had at the moment his feet touched the ground, which is the same as the velocity he had when he was 2.89 m above the ground, so his initial velocity is zero. His final velocity is also zero, since he comes to rest. Therefore, the change in velocity is zero. Since the change in velocity is zero, the vertical acceleration is also zero. The average force exerted on the ground is equal to the mass of the man multiplied by the vertical acceleration, so the average force is zero.