A man with a mass of 80KG stands on a bathroom scale on the floor of a lift. Determine the reading of the scale if the lift is at freefall.
F = m a
F up from scale - m g = m a
but a = -g (free fall)
so
F up from scale - m g = - mg
so
F up from scale = 0
To determine the reading of the scale, we need to consider the forces acting on the man in the freefalling lift.
When the lift is at freefall, it means that the lift is accelerating downward at the same rate as gravity (9.8 m/s^2). In this situation, the man and the scale are both accelerating downward as well.
Now, let's examine the forces acting on the man in the lift:
1. Weight force: This is the force due to the man's mass pulling downward towards the center of the Earth. It can be calculated using the formula: Weight = mass × acceleration due to gravity.
In this case, the weight of the man is:
Weight = 80 kg × 9.8 m/s^2 ≈ 784 N (rounded to the nearest whole number)
2. Normal force: This is the force exerted by the scale on the man, perpendicular to the surface of the scale. In a normal situation (not freefall), the normal force would be equal in magnitude and opposite in direction to the weight force, resulting in no net force and a constant reading on the scale.
However, in the case of freefall, the acceleration of the lift affects the normal force. As the lift accelerates downward, it reduces the effect of the gravitational force, resulting in a decrease in the normal force.
Since the man is in freefall with the lift, the normal force exerted by the scale on the man is zero when the lift is at freefall. This means that the reading on the scale will be zero.
So, the reading of the bathroom scale when the lift is at freefall would be 0 N.