A man whose mass is 80kg stands on a weighing machine inside a lift: when the lift starts accelerating upwards, the reading of the weighing machine was observed to be 96kg. Determine the upward acceleration of the lift?

Need the working for that question

A man whose mass is 80kg stands on a weighing machine inside the lift. When the lift start accelerating upward the reading of the weighing machine was observed at 96kg determine the upward acceleration

bisola

I want the answer for this question please

How can this be solved

To determine the upward acceleration of the lift, we need to understand the forces acting on the man inside the lift.

1. First, let's consider the forces acting on the man when he is at rest:
- Weight (mg): This is the force due to gravity acting on the man. Its magnitude can be calculated using the formula weight = mass × gravitational acceleration, where the gravitational acceleration is approximately 9.8 m/s^2.

In this case, the man's weight will be: weight = 80 kg × 9.8 m/s^2 = 784 N.

2. Now, let's consider the forces acting on the man when the lift starts accelerating upwards:
- Normal force (N): This is the force exerted by the weighing machine on the man, perpendicular to the surface. In this case, the normal force balances out the weight of the man. So, when acceleration is present, the normal force will be greater than the man's weight in order to balance out the forces.

The observed reading on the weighing machine is 96 kg. We can convert this reading to Newtons by multiplying it by the gravitational acceleration:
96 kg × 9.8 m/s^2 = 940.8 N.

Therefore, the normal force acting on the man inside the lift when it is accelerating upwards is 940.8 N.

3. Next, let's calculate the net force acting on the man:
Net force (F_net) = Normal force (N) - Weight (mg)

F_net = 940.8 N - 784 N = 156.8 N

4. Finally, we can use Newton's second law of motion to calculate the upward acceleration of the lift:
F_net = mass × acceleration

Rearranging the equation, we get:
acceleration = F_net / mass

acceleration = 156.8 N / 80 kg = 1.96 m/s^2

Therefore, the upward acceleration of the lift is approximately 1.96 m/s^2.