An elevator accelerates upward at 1.2 m/s
2
.
The acceleration of gravity is 9.8 m/s
2
.
What is the upward force exerted by the
floor of the elevator on a(n) 72 kg passenger?
Answer in units of N.
the upward acceleration of the elevator adds to the gravitational force
f = m a = 72 kg * (9.8 m/s^2 + 1.2 m/s^2)
So it would be 72*11=792?
yup
To calculate the upward force exerted by the floor of the elevator on a passenger, we need to consider the net force acting on the passenger. The net force is the difference between the force of gravity and the force exerted by the floor.
1. First, let's calculate the force of gravity acting on the passenger. The force of gravity can be calculated using the equation:
`force_gravity = mass * acceleration_gravity`
Given:
- Mass (m) = 72 kg
- Acceleration due to gravity (acceleration_gravity) = 9.8 m/s^2
Applying the values, we get:
`force_gravity = 72 kg * 9.8 m/s^2 = 705.6 N`
Therefore, the force of gravity acting on the passenger is 705.6 Newtons.
2. The upward force exerted by the floor of the elevator can be calculated as the net force acting on the passenger. The net force is given by the equation:
`net_force = mass * acceleration`
Given:
- Mass (m) = 72 kg
- Acceleration (acceleration) = 1.2 m/s^2 (upward acceleration)
Applying the values, we get:
`net_force = 72 kg * 1.2 m/s^2 = 86.4 N`
This is the net force exerted on the passenger by the floor of the elevator.
3. However, remember that the net force is the difference between the force of gravity and the force exerted by the floor. Therefore, the upward force exerted by the floor of the elevator on the passenger is:
`upward_force = net_force - force_gravity`
Applying the values, we have:
`upward_force = 86.4 N - 705.6 N = -619.2 N`
Note: The negative sign indicates that the force is exerted upward.
Therefore, the upward force exerted by the floor of the elevator on the 72 kg passenger is 619.2 Newtons.