A man of mass 70,000 Gram on the ground is standing in an elevator. Find the Page 3 of 12 force extracted by the man on the floor of the elevator when it (i) is at rest, (ii) moves up with an acceleration of 3.5 m/s², (iii) moves down with an acceleration of 4.5 m/s².

(i) When the elevator is at rest, the force exerted by the man on the floor of the elevator is simply his weight. This is calculated by multiplying his mass by the acceleration due to gravity.

The man's mass is 70,000 grams, which is equivalent to 70 kg (since 1 kg = 1000 grams). The acceleration due to gravity is approximately 9.8 m/s².

So, the force (F) = mass (m) x acceleration due to gravity (g) = 70 kg x 9.8 m/s² = 686 N (Newtons).

(ii) When the elevator is moving upwards with an acceleration of 3.5 m/s², the force exerted by the man on the floor of the elevator is his weight plus the force due to the upward acceleration.

The force due to the upward acceleration is calculated by multiplying his mass by the acceleration of the elevator.

So, the additional force = mass x acceleration = 70 kg x 3.5 m/s² = 245 N.

Therefore, the total force when the elevator is moving upwards = weight + additional force = 686 N + 245 N = 931 N.

(iii) When the elevator is moving downwards with an acceleration of 4.5 m/s², the force exerted by the man on the floor of the elevator is his weight minus the force due to the downward acceleration.

The force due to the downward acceleration is calculated by multiplying his mass by the acceleration of the elevator.

So, the reduced force = mass x acceleration = 70 kg x 4.5 m/s² = 315 N.

Therefore, the total force when the elevator is moving downwards = weight - reduced force = 686 N - 315 N = 371 N.

(i) When the elevator is at rest, the force exerted by the man on the floor of the elevator is simply his weight. This is calculated by multiplying his mass by the acceleration due to gravity.

The man's mass is 70,000 grams, which is equivalent to 70 kg (since 1 kg = 1000 grams). The acceleration due to gravity is approximately 9.8 m/s².

So, the force (F) = mass (m) x acceleration due to gravity (g) = 70 kg x 9.8 m/s² = 686 N (Newtons).

(ii) When the elevator is moving upwards with an acceleration of 3.5 m/s², the force exerted by the man on the floor of the elevator is his weight plus the force due to the upward acceleration.

So, the force (F) = mass (m) x (acceleration due to gravity (g) + acceleration of the elevator (a)) = 70 kg x (9.8 m/s² + 3.5 m/s²) = 70 kg x 13.3 m/s² = 931 N.

(iii) When the elevator is moving downwards with an acceleration of 4.5 m/s², the force exerted by the man on the floor of the elevator is his weight minus the force due to the downward acceleration.

So, the force (F) = mass (m) x (acceleration due to gravity (g) - acceleration of the elevator (a)) = 70 kg x (9.8 m/s² - 4.5 m/s²) = 70 kg x 5.3 m/s² = 371 N.