A 75.0-kg person stands on a scale in an elevator. What does the scale read (in N) when the elevator is at rest? What does the scale read (in N) when the elevator is climbing at a constant speed of 3.0 m/s? What does the scale read (in N) when the elevator is descending at 3.0 m/s? What does the scale read (in N) when the elevator is accelerating upward at 2.5 m/s2 ? What does the scale read (in N) when the elevator is accelerating downward at 2.5 m/s2 ?
on earth
at rest
75 kg * 9.8 m/s^2 = x Newtons
at constant speed, no acceleration, still the same 75*9.81
still at constant speed down, still the same
acc up = 2.5 m/s^2, now we are getting somewhere
net Force up on person = m * 2.5 m/s^2
weight force down on person = m g = m * 9.8
scale force up - m g = m a
scale force up = m (g+a) = 75 ( 9.8 + 2.5)
if a = -2.5 then
75 (9.8 - 2.5)
Incorrect answer, Gravity is a downward force therefore it is -9.8 or -9.81. You do -9.81-2.5 and then multiply it out.
Ahh, the good old elevator physics problem! Let's dive into it with a touch of humor, shall we?
When the elevator is at rest, the scale reads the usual weight of the person, which is their mass (75.0 kg) multiplied by the acceleration due to gravity (9.8 m/s²). So, the scale reads 75.0 kg × 9.8 m/s². But since I'm a clown bot and can't do calculations, let's just say the scale reads "Gravity-approved weight: Heavy enough to make your mom proud!"
Now, when the elevator is climbing at a constant speed of 3.0 m/s, there's no vertical acceleration. So, the scale reads the same as at rest, because the person's weight doesn't change. Ah, the joys of inertia! The scale says, "No extra weight to carry, just the burden of life!"
But when the elevator is descending at 3.0 m/s, again with no vertical acceleration, the scale reads the same as at rest or while climbing. The person's weight remains unchanged, making the scale say, "Down we go, but your weight stays put!"
Now, let's spice things up a bit! When the elevator is accelerating upward at 2.5 m/s², the scale reads the person's mass multiplied by the net force acting on them. The net force is the sum of their weight and the force due to acceleration. So the scale says, "Hold on tight! Your weight plus the 'going up' force!"
Conversely, when the elevator is accelerating downward at 2.5 m/s², the scale reads the person's mass multiplied by the net force acting on them. This time, the net force is the difference between their weight and the force due to acceleration. The scale shouts, "Gravity meets a push! Your weight minus the 'going down' force!"
Remember, these are all simplified explanations, but I hope they put a smile on your face while learning about the readings on the scale.
To solve this problem, we need to consider the various forces acting on the person in each scenario. Let's break it down step by step.
1. When the elevator is at rest:
In this situation, the person and the elevator are not accelerating, meaning the net force acting on the person is zero. Therefore, the scale reading will be equal to the person's weight, which can be calculated using the formula:
Weight = mass * acceleration due to gravity (g)
Weight = 75.0 kg * 9.8 m/s^2
Weight = 735 N
The scale will read 735 N when the elevator is at rest.
2. When the elevator is climbing at a constant speed of 3.0 m/s:
If the elevator is moving at a constant speed, the person and the elevator will still experience the same net force. Therefore, the scale reading will remain the same as when the elevator is at rest, which is 735 N.
3. When the elevator is descending at 3.0 m/s:
Similar to the previous case, when the elevator is moving at a constant speed, the scale reading remains the same. Hence, the scale will read 735 N.
4. When the elevator is accelerating upward at 2.5 m/s^2:
In this case, we need to consider the additional force due to the upward acceleration of the elevator. The scale reading will be equal to the sum of the person's weight and the upward force due to acceleration. The formula to calculate this is:
Scale Reading = Weight + (mass * acceleration)
Weight = 75.0 kg * 9.8 m/s^2
Weight = 735 N
Scale Reading = 735 N + (75.0 kg * 2.5 m/s^2)
Scale Reading = 735 N + 187.5 N
Scale Reading = 922.5 N
The scale will read 922.5 N when the elevator is accelerating upward at 2.5 m/s^2.
5. When the elevator is accelerating downward at 2.5 m/s^2:
Here, we consider the additional force due to the downward acceleration of the elevator. The scale reading will be the difference between the person's weight and the downward force due to acceleration. Using the same formula as before:
Scale Reading = Weight - (mass * acceleration)
Scale Reading = 735 N - (75.0 kg * 2.5 m/s^2)
Scale Reading = 735 N - 187.5 N
Scale Reading = 547.5 N
The scale will read 547.5 N when the elevator is accelerating downward at 2.5 m/s^2.