A person weighs 150 pounds. He is standing on a scale in an elevator and stands on a scale. The elevator is accelerating upwards at a rate of 10 m/s/s, what is the reading of the scale?
150 pounds
about 75 pounds
about 300 pounds
not enough info
Would it be 300 pounds?
F = m a
150 lbs = 68 kg
Fscale up - m g down = m a
Fscale up = m g + m a
= 150 pounds + 68* 10 newtons
= 150 pounds + 680 Newtons
680 Newtons = 153 pounds
so 150 + 153 is about 300 pounds
To determine the reading of the scale, we need to consider the forces acting on the person in the elevator.
When the elevator is at rest or moving with a constant velocity, the person's weight is balanced by the normal force exerted by the scale. In this case, the scale would read 150 pounds (assuming no other forces are present).
However, in this scenario, the elevator is accelerating upwards at a rate of 10 m/s^2. This acceleration increases the normal force on the person, resulting in an apparent increase in weight.
To calculate the reading of the scale, we can use the concept of apparent weight. The apparent weight of an object is the force exerted by the scale on the object.
The formula for calculating the apparent weight is:
Apparent weight = actual weight + (mass × acceleration)
First, let's convert the weight from pounds to mass in kilograms. We know that 1 pound is approximately equal to 0.454 kilograms.
Weight = 150 pounds × 0.454 kg/pound = 68.1 kg
Now that we have the weight in kilograms, we can plug in the values into the formula:
Apparent weight = 68.1 kg + (68.1 kg × 10 m/s^2)
Apparent weight = 68.1 kg + 681 kg m/s^2
Apparent weight = 749.1 kg m/s^2
Finally, let's convert the apparent weight back to pounds:
Apparent weight = 749.1 kg m/s^2 × 2.205 pounds/kg
Apparent weight ≈ 1656.4 pounds
Therefore, the reading of the scale in this scenario would be approximately 1656.4 pounds.