A child with a mass of 39 kg stands on a spring scale inside an elevator. For each of the scenarios below, draw a force diagram of the forces acting on the child and calculate the reading of the scale in newtons.

(a) The elevator is at rest.

_______ N

(b) The elevator is accelerating downward at 1 m/s2.

_______ N

(c) The elevator is moving upward at a constant velocity of 9 m/s.

________N

(d) The elevator is accelerating upward at 3 m/s2.

_______ N

To find the reading of the spring scale in each scenario, we need to analyze the forces acting on the child in the elevator. Here's how to calculate it for each case:

(a) The elevator is at rest:
When the elevator is at rest, the child experiences two forces:
- The force due to gravity (weight), which acts vertically downwards with a magnitude of mg, where m is the mass of the child (39 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- The normal force exerted by the scale, which acts vertically upwards and cancels out the weight.

Since the elevator is at rest, there is no acceleration, so the normal force must be equal to the weight:

Normal force = Weight = mg

Substituting the values:
Normal force = 39 kg * 9.8 m/s^2 = 382.2 N

The reading on the scale will be 382.2 N, upwards.

(b) The elevator is accelerating downward at 1 m/s^2:
In this scenario, the child experiences the following forces:
- The force due to gravity (weight), which acts vertically downwards with a magnitude of mg.
- The force exerted by the scale, which acts vertically upwards and cancels out the weight.
- The force of acceleration, which acts vertically downward and is given by ma, where m is the mass of the child (39 kg) and a is the acceleration of the elevator (-1 m/s^2). Note that we use a negative sign for the acceleration because it is downward.

To find the reading on the scale, we need to calculate the net force acting on the child:
Net force = Force due to gravity + Force of acceleration

Net force = mg + ma

Substituting the values:
Net force = (39 kg * 9.8 m/s^2) + (39 kg * -1 m/s^2) = 382.2 N - 39 N = 343.2 N

The reading on the scale will be 343.2 N, upwards.

(c) The elevator is moving upward at a constant velocity of 9 m/s:
When the elevator is moving at a constant velocity, the child experiences the following forces:
- The force due to gravity (weight), which acts vertically downwards with a magnitude of mg.
- The force exerted by the scale, which acts vertically upwards and cancels out the weight.
- No additional force since there is no acceleration.

Since there is no acceleration, the net force acting on the child is zero. Therefore, the reading on the scale will be equal to the weight:

Reading on the scale = Weight = mg

Substituting the values:
Reading on the scale = 39 kg * 9.8 m/s^2 = 382.2 N

The reading on the scale will be 382.2 N, upwards.

(d) The elevator is accelerating upward at 3 m/s^2:
In this scenario, the child experiences the following forces:
- The force due to gravity (weight), which acts vertically downwards with a magnitude of mg.
- The force exerted by the scale, which acts vertically upwards and cancels out the weight.
- The force of acceleration, which acts vertically upwards and is given by ma, where m is the mass of the child (39 kg) and a is the acceleration of the elevator (3 m/s^2).

To find the reading on the scale, we need to calculate the net force acting on the child:
Net force = Force due to gravity + Force of acceleration

Net force = mg + ma

Substituting the values:
Net force = (39 kg * 9.8 m/s^2) + (39 kg * 3 m/s^2) = 382.2 N + 117 N = 499.2 N

The reading on the scale will be 499.2 N, upwards.