How much force is required to lift a box of weight 100 N upwards with a constant acceleration of 6.0 m/s2?

Question

a. How much force is required to lift a box of weight 100 N upwards with a constant acceleration of 6.0 m/s²?

b. How much upwards force is required to lower the same box with a downward acceleration of 3.0 m/s²?

Answer 1

a. How much force is required to lift a box of weight 100 N upwards with a constant acceleration of 6.0 m/s²?

b. How much upwards force is required to lower the same box with a downward acceleration of 3.0 m/s²?

a. As the box weighs 100 N, its mass is 100 N / 9.8 ms^-2 = 10.2 kg. To have an upward acceleration of 6.0 m/s², there must be a net upward force of F =ma = 10.2 kg x 6.0 m/s² = 61.2 N. The total upward force must be equal have a magnitude to overcome the downward force of gravity and to provide for the upward acceleration F_{total up} = 100 N + 61.2 N = 161.2 N.

b. There must be a net downward force F = ma = 10.2 kg x 3.0 m/s² = 30.6 N upward. There must be an upward force to counteract the downward force of gravity so that the resultant will be 30.6 N. The equation necessary for this is 100 N - upward force = 30.6 N. Solving for the upward force gives 69.4 N.