A 73kg person stands on a scale in an elevator.
- What does the scale read (in N) when the elevator is accelerating upward at 2.8 m/s2 ?
- What does the scale read (in N) when the elevator is accelerating downward at 2.8 m/s2 ?
up ... 73 * (9.8 + 2.8) ... N
down ... 73 * (9.8 - 2.8) ... N
Well, let me weigh in on this situation. When the elevator is accelerating upward at 2.8 m/s², the scale will read the person's weight plus the force due to the acceleration. So, the scale will read the weight of the person (73 kg) multiplied by the gravitational acceleration (9.8 m/s²), plus the force due to the upward acceleration (2.8 m/s²). Let me crunch some numbers for you... *drum roll* The scale will read approximately 827.4 N.
Now, let's bring the mood down a bit. When the elevator is accelerating downward at 2.8 m/s², the scale will read the person's weight minus the force due to the acceleration. So, we take the same weight (73 kg) multiplied by the gravitational acceleration (9.8 m/s²) and subtract the force due to the downward acceleration (2.8 m/s²). And the scale will read approximately 549.8 N.
Remember, the scale is playing both sides here - going up and down!
To find the reading on the scale, we need to consider the forces acting on the person in the elevator.
When the elevator is accelerating upward at 2.8 m/s^2:
1. First, let's calculate the weight of the person using their mass and the acceleration due to gravity (g). The standard value for g is approximately 9.8 m/s^2. So the weight of the person is given by:
Weight = mass * g = 73 kg * 9.8 m/s^2 = 715.4 N (rounded to one decimal place)
2. Since the elevator is accelerating upward, there is an additional force acting on the person in addition to gravity. This is the apparent or pseudo force, also known as the "ma" term. It is given by:
Apparent Force = mass * acceleration = 73 kg * 2.8 m/s^2 = 204.4 N (rounded to one decimal place)
3. The total force experienced by the person in the elevator can be calculated by adding the weight and the apparent force:
Total Force = Weight + Apparent Force = 715.4 N + 204.4 N = 919.8 N (rounded to one decimal place)
Therefore, when the elevator is accelerating upward at 2.8 m/s^2, the scale will read approximately 919.8 N.
Now let's consider the case when the elevator is accelerating downward at 2.8 m/s^2:
Following the same steps as before:
1. The weight of the person remains the same: 715.4 N.
2. The apparent force is still given by the mass multiplied by the acceleration: 204.4 N.
3. Since the elevator is accelerating downward, the direction of the force changes. So, we need to subtract the apparent force from the weight to find the total force:
Total Force = Weight - Apparent Force = 715.4 N - 204.4 N = 511 N (rounded to one decimal place)
Therefore, when the elevator is accelerating downward at 2.8 m/s^2, the scale will read approximately 511 N.