A body hangs from a spring balance supported from the roof of an elevator. If the elevator has an upward acceleration of
3ms−2
and the balance reads 50 N, what is the true weight of the body?
To find the true weight of the body, we need to account for the upward acceleration of the elevator.
Step 1: Identify the forces acting on the body.
When the body is stationary or the elevator is moving at a constant velocity, the only force acting on it is the gravitational force, which is equal to its weight.
However, in this case, the elevator is accelerating upward, meaning there must be an additional force acting on the body. This force is the apparent weight measured by the spring balance.
Step 2: Calculate the apparent weight of the body.
The apparent weight is the force experienced by the body due to acceleration. It can be calculated using the following equation:
Apparent weight = True weight + ma
where m is the mass of the body and a is the acceleration.
In this case, the apparent weight is given as 50 N and the upward acceleration is 3 m/s^2. We need to solve for the true weight.
Step 3: Rearrange the equation to solve for the true weight.
True weight = Apparent weight - ma
Step 4: Plug in the given values and calculate the true weight.
True weight = 50 N - (m)(3 m/s^2)
Since we don't have the mass of the body, we cannot determine the true weight without it. If the mass is known, you can substitute its value into the equation to calculate the true weight.