A 102-kg man stands in an elevator that has an upward acceleration of 4.1 m/s2. The magnitude of the force exerted by him on the floor is about (g = 10 m/s2):
To find the magnitude of the force exerted by the man on the floor, we need to consider the two forces acting on him: his weight and the net force exerted by the elevator.
1. Calculate the weight of the man:
The weight of an object can be calculated using the formula: weight = mass * acceleration due to gravity (g).
Here, the mass of the man is given as 102 kg, and the acceleration due to gravity is 10 m/s^2.
So, the weight of the man will be: weight = 102 kg * 10 m/s^2 = 1020 N.
2. Calculate the net force exerted by the elevator:
The net force exerted on an object is calculated using the formula: net force = mass * acceleration.
Here, the mass of the man is 102 kg, and the acceleration of the elevator is given as 4.1 m/s^2.
So, the net force exerted by the elevator will be: net force = 102 kg * 4.1 m/s^2 = 418.2 N.
3. Determine the magnitude of the force exerted by the man on the floor:
The force exerted by the man on the floor will be equal in magnitude but opposite in direction to the net force exerted by the elevator. Therefore, the magnitude of the force exerted by the man will also be 418.2 N.
So, the magnitude of the force exerted by the man on the floor is approximately 418.2 N.