an 800 N person stands on a scale in an elevator. What is his apparent weight when the elevator is accelerating upward at 2 m/s^2? B) what5 is his apparent weight when the elevator is acc. downward at 2m/s^2? c) what is his apparent weight when the elevator is moving downward at a constant velocity of 2m/s^2?
Try setting up a force balance on the person. "The apparent weight" W is the force that would act upward from a measuring scale or the floor, and the true weight M g acts downwards.
According to Newton's second law,
W - M g = M a, is a is measured postive upwards.
All three parts of the problem can be solved with this equation. a = +2 m/s^2 in (a), -2 m/s^2 in (b) and 0 in (c). Solve for W in each case.
Boom Boom
To solve this problem, we can use Newton's second law and set up a force balance on the person. The apparent weight, W, is the force that would act upward from a measuring scale or the floor, and the true weight, Mg, acts downwards.
According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the difference between the apparent weight and the true weight, and the acceleration is the acceleration of the elevator.
So, the equation we can set up is:
W - Mg = Ma
In part (a) of the problem, the elevator is accelerating upward at 2 m/s^2. Substituting the values into the equation, we have:
W - Mg = M * 2
Simplifying the equation, we get:
W = M * (2 + g)
Since the true weight, Mg, is equal to 800 N, we can substitute that value into the equation:
W = M * (2 + g) = 800
Now, we can solve for W:
800 = M * (2 + 9.8)
800 = M * 11.8
Dividing both sides of the equation by 11.8, we find:
M ≈ 67.8 kg
Now, substitute this value of M back into the equation to find W:
W = 67.8 * (2 + 9.8)
W ≈ 800 N
So, the person's apparent weight when the elevator is accelerating upward at 2 m/s^2 is approximately 800 N.
Similarly, you can follow the same steps for parts (b) and (c) of the problem, but with different accelerations.
In part (b), the elevator is accelerating downward at 2 m/s^2. So the equation becomes:
W - Mg = M * (-2)
Substitute the known values and solve for W.
In part (c), the elevator is moving downward with a constant velocity of 2 m/s^2. In this case, the acceleration is 0, so the equation becomes:
W - Mg = M * 0
Solve for W using the known values.
Following these steps, you can find the apparent weight of the person in each scenario.
Let's solve each part of the problem step by step:
a) When the elevator is accelerating upward at 2 m/s^2, we can use the equation W - M * g = M * a, where W is the apparent weight, M is the mass of the person, g is the acceleration due to gravity (approximately 9.8 m/s^2), and a is the acceleration of the elevator.
Given that the person's weight (true weight) is 800 N, we know that M * g = 800 N. Plugging this into the equation, we have:
W - 800 = M * 2
To solve for W, we need to know the mass of the person. Since weight is given in Newtons (N), we can use the equation W = M * g, where g = 9.8 m/s^2. Rearranging this equation, we get M = W / g.
M = 800 N / 9.8 m/s^2 ≈ 81.63 kg
Now we can substitute this mass value into the equation above:
W - 800 = 81.63 kg * 2
W - 800 = 163.26 N
W = 963.26 N
Therefore, the person's apparent weight when the elevator is accelerating upward at 2 m/s^2 is approximately 963.26 N.
b) When the elevator is accelerating downward at 2 m/s^2, we can use the same equation: W - M * g = M * a.
In this case, the acceleration a is -2 m/s^2 (negative because it is downward). Using the same approach as in part (a), we find:
W - 800 = 81.63 kg * (-2)
W - 800 = -163.26 N
W = 636.74 N
Therefore, the person's apparent weight when the elevator is accelerating downward at 2 m/s^2 is approximately 636.74 N.
c) When the elevator is moving downward at a constant velocity of 2 m/s^2, there is no acceleration (a = 0). The equation becomes:
W - M * g = M * 0
W - 800 = 0
W = 800 N
Therefore, the person's apparent weight when the elevator is moving downward at a constant velocity of 2 m/s^2 is equal to their true weight, which is 800 N.