An elevator's cable is cut causing the elevator to slide down thhe elevator shaft on the emergency brakes and wheels. Suppose that the mass of the elevator and passengers were 1500 kg, and the frictional force (wheels on tracks)was 9000N

Draw a force diagram

determine the acceleration of the elevator

Suppose that a 50.0kg woman were standing on a bathroom scale in this elevatorcar. what would the scale read?

Determine how long it would take for the elevator car(starting from rest)to drop 30 floors (assume each floor is 3.0m)

To answer these questions, we need to analyze the forces acting on the elevator and use Newton's laws of motion.

1. Force Diagram:
The force diagram for the elevator includes the weight (mg) acting downwards, the normal force (N) acting upwards, the frictional force (Ff) acting in the opposite direction of motion, and the tension force (T) in the cable (which is zero since the cable is cut).


N │

─────Elevator───

mg │ Ff


2. Acceleration of the Elevator:
The net force on the elevator is the difference between the weight (mg) and the frictional force (Ff). Using Newton's second law (F = ma), we can write the equation: mg - Ff = ma, where m is the mass of the elevator and passengers, and a is the acceleration of the elevator. Rearranging the equation, we get a = (mg - Ff) / m. Substituting the given values, we have a = (1500 kg * 9.8 m/s^2 - 9000 N) / 1500 kg. Solving this equation will give us the acceleration.

3. Reading on the Bathroom Scale:
When the elevator is moving downward, the normal force decreases. The reading on the bathroom scale is equal to the net force acting on the woman. In this case, the net force is the difference between the woman's weight (mg) and the normal force (N). Therefore, the reading on the bathroom scale will be mg - N. Substituting the given values, we can calculate the reading on the scale.

4. Time to Drop 30 Floors:
To determine the time taken to drop 30 floors, we need to find the distance traveled by the elevator first. Since each floor has a height of 3.0 m, the total distance traveled can be calculated as 30 floors * 3.0 m/floor. Once we have the distance traveled, we can use the kinematic equation s = ut + (1/2)at^2, where s is the distance, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time it takes to travel the distance. By rearranging this equation, we can solve for the time (t).

By following these explanations, you should be able to find the answers to the given questions.

Force diagram:

1. Weight force (mg) acting downwards
2. Normal force (N) acting upwards
3. Frictional force (Ff) acting upwards (opposing motion)
4. Tension force (T) acting upwards in the cable (before it was cut)

Acceleration of the elevator:

To determine the acceleration of the elevator, we need to consider the net force acting on it. The net force is given by the difference between the downward weight force and the upward frictional force:

Net force = mg - Ff

Substituting the given values:
Mass (m) = 1500 kg
Weight force (mg) = 1500 kg * 9.8 m/s^2 = 14700 N
Frictional force (Ff) = 9000 N

Net force = 14700 N - 9000 N = 5700 N

Using Newton's second law (F = ma), we can rearrange it to solve for acceleration (a):

a = Net force / Mass
= 5700 N / 1500 kg
= 3.8 m/s^2

Thus, the acceleration of the elevator is 3.8 m/s^2.

Scale reading:

When the elevator is in free fall (cable is cut), both the elevator and the scale experience the same acceleration. Since the scale supports the woman's weight, the scale reading will be equal to the normal force exerted by the woman on the scale.

Normal force (N) = Weight force (mg)
= 50.0 kg * 9.8 m/s^2
= 490 N

Therefore, the scale reading would be 490 N.

Time to drop 30 floors:

Each floor has a height of 3.0 m, so to drop 30 floors, the distance traveled is:

Distance = 30 floors * 3.0 m/floor
= 90 m

We know the initial velocity (u) is 0 m/s (starting from rest) and the final velocity (v) can be found using the kinematic equation:

v^2 = u^2 + 2ad

Rearranging the equation to solve for time (t):

t = (v - u) / a

Given that the final velocity (v) is the speed acquired after dropping 90 m and the initial velocity (u) is 0 m/s, we can calculate the time (t):

v^2 = 0 + 2ad
v^2 = 2ad
√(2ad) = v

v = √(2 * 3.8 m/s^2 * 90 m)
= √684 m^2/s^2
= 26.2 m/s

t = (26.2 m/s - 0 m/s) / 3.8 m/s^2
= 6.89 s

Therefore, it would take approximately 6.89 seconds for the elevator car to drop 30 floors.