What is the acceleration of an elevator if the mass of the elevator and occupants is 1200 kg and the tension in the cable is 10000 N? Which direction is the elevator going?
cable exerts an upward force
gravity exerts a downward force
find the net force
a = f / m
To find the acceleration of the elevator, we can use the equation of motion for a single body:
F = m * a
Here,
F is the net force acting on the elevator,
m is the mass of the elevator and occupants,
a is the acceleration of the elevator.
In this case, the tension in the cable provides the net force (F). So we can rewrite the equation as:
Tension = m * a
Given:
Mass (m) = 1200 kg
Tension (T) = 10000 N
Plugging in the values, we get:
10000 N = 1200 kg * a
Solving for 'a':
a = 10000 N / 1200 kg
a ≈ 8.33 m/s²
Therefore, the acceleration of the elevator is approximately 8.33 m/s².
To determine the direction the elevator is moving, we need to consider the sign of the acceleration. Since the tension in the cable is greater than the force of gravity pulling the elevator downwards, we can conclude that the elevator is moving upward.