An elevator and rider have a mass of 1600 kg combined. What is the tension force in the cable lifting them at a steady speed of 3 m/s? Assume no friction.
To determine the tension force in the cable lifting the elevator and rider, you need to consider the forces acting on the system at a steady speed of 3 m/s.
1. Start by calculating the gravitational force acting on the elevator and rider. This force can be found using the formula:
Force_gravity = mass * acceleration_due_to_gravity
The acceleration due to gravity on Earth is approximately 9.8 m/s². Therefore:
Force_gravity = 1600 kg * 9.8 m/s²
2. Next, consider the net force acting on the system. Since the elevator is moving at a steady speed, the net force must be zero. The net force is the difference between the upward force exerted by the tension in the cable and the downward force of gravity:
Net_force = Tension_force - Force_gravity
Setting the net force to zero:
0 = Tension_force - Force_gravity
Tension_force = Force_gravity
3. Substitute the calculated value of the gravitational force into the equation:
Tension_force = 1600 kg * 9.8 m/s²
Tension_force ≈ 15,680 N
Therefore, the tension force in the cable lifting the elevator and rider at a steady speed of 3 m/s is approximately 15,680 Newtons.