A passenger with mass of 80 kg stands on the floor of an elevator of mass 250 kg as it accelerates upward with an acceleration of 3 m/s^2. Determine the tension in the elevator cable. Draw a free-body diagram.
1. Determine the total force acting downwards. Calculate the force of gravity acting on the passenger and the elevator.
F = m * a
Ft + Fg = 330kg * 3m/s^2
Solve for Ft?
4224N
To determine the tension in the elevator cable, we can start by drawing a free-body diagram of the passenger.
Free body diagram of the passenger:
- There is a downward force due to gravity (weight) acting on the passenger, which is given by W = m * g, where m is the mass of the passenger (80 kg) and g is the acceleration due to gravity (typically 9.8 m/s^2).
Next, let's consider the free-body diagram for the elevator:
Free body diagram of the elevator:
- There is an upward force due to the tension in the cable.
- There is a downward force due to the weight of the elevator, which is given by W = m * g, where m is the mass of the elevator (250 kg) and g is the acceleration due to gravity (typically 9.8 m/s^2).
- There is also a net upward force acting on the elevator, which is equal to the mass of the elevator multiplied by its acceleration (F = m * a). Here, the acceleration is the same as the given 3 m/s^2.
Since the elevator is accelerating upwards, the tension in the cable must be greater than the sum of the weights of the passenger and the elevator.
Using these considerations, we can write the equation for the net upward force acting on the elevator:
F_net = Tension - Weight of elevator
= m_elevator * a
= 250 kg * 3 m/s^2
= 750 N
Since we also know the weight of the elevator, we can add it to the equation:
F_net = Tension - (m_elevator * g)
= 750 N
Tension = 750 N + (m_elevator * g)
= 750 N + (250 kg * 9.8 m/s^2)
= 750 N + 2450 N
= 3200 N
Therefore, the tension in the elevator cable is 3200 N.
To determine the tension in the elevator cable, we need to analyze the forces acting on the passenger and the elevator.
First, let's draw a free-body diagram for the passenger and the elevator. The free-body diagram shows all the forces acting on the objects involved.
For the passenger:
1. Gravitational force (Weight) acting downward, given by Fg = m * g, where m is the mass of the passenger and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Normal force acting upward, exerted by the floor of the elevator. This force cancels out the gravitational force.
3. Tension in the elevator cable acting upward.
For the elevator:
1. Gravitational force (Weight) acting downward, given by Fg = m * g, where m is the mass of the elevator and g is the acceleration due to gravity.
2. Tension in the elevator cable acting upward.
3. Normal force exerted by the passenger. This force cancels out the gravitational force.
Now, let's determine the magnitudes of these forces and find the tension in the elevator cable.
For the passenger:
Gravitational force (Weight) = m * g = 80 kg * 9.8 m/s^2 = 784 N
Normal force = Gravitational force = 784 N (since the passenger is standing on the floor and is not accelerating vertically)
Tension in the elevator cable = Gravitational force + Normal force = 784 N + 784 N = 1568 N
For the elevator:
Gravitational force (Weight) = m * g = 250 kg * 9.8 m/s^2 = 2450 N
Normal force = Gravitational force + Tension in the elevator cable = 2450 N + 1568 N = 4018 N
Tension in the elevator cable = Normal force - Gravitational force = 4018 N - 2450 N = 1568 N
Therefore, the tension in the elevator cable is 1568 N.