A 50 kg passenger is travelling in a 700 kg (NOT including the passenger) elevator. The passenger notices that her apparent weight is 950 N. What is the tension in the wire holding the elevator?
First, we can find the gravitational force acting on the passenger using the formula F = mg, where m is the mass and g is the gravitational acceleration (approximately 9.81 m/s^2):
F_p = (50 kg)(9.81 m/s^2) = 490.5 N
Since the apparent weight is greater than the true gravitational force acting on the passenger, the elevator is accelerating upward. We can find the acceleration by using the formula W = mg + ma, where W is the apparent weight, m is the mass, g is the gravitational acceleration, and a is the acceleration:
950 N = (50 kg)(9.81 m/s^2) + (50 kg)(a)
Divide both sides by 50 kg:
19 N/kg = 9.81 N/kg + a
Subtract 9.81 N/kg from both sides:
a = 9.19 m/s^2
Now we can find the total force acting on the elevator, including the passenger, using F = ma:
F_total = (750 kg)(9.19 m/s^2) = 6,892.5 N
This force includes the gravitational force acting on the passenger and the elevator, so the tension in the wire holding the elevator is equal to the total force acting on the elevator:
Tension = F_total = 6,892.5 N