Question

The brakes on an elevator of weight 50,000 N act upward with a force of 100,000 N The acceleration of elevator while braking would be

Answer 1

9.8 m/s² up

Step-by-step explanation

Given:

• The elevator's weight, Fg = 50,000 N

,

• The upward force acting on the elevator, F = 100,000 N

Find:

• The elevator's acceleration, a

By Newton's second law of motion, the net force acting on an object of mass m is,

`F_(net)=m\cdot a`

In this case, there are two forces acting on the elevator: the upward force of the brakes and the downward force of the elevator's weight, so the net force is,

`F-F_g=m\cdot a`

We can find the mass of the elevator from its weight, knowing that g = 9.8 m/s²,

`F_g=m\cdot g\Rightarrow m=(F_g)/(g)=\frac{50,000N}{9.8\text{ }m/s²}\approx5102.04\text{ }kg`

Solving the net-force equation for a,

`a=(F-F_g)/(m)`

Replace the known values and solve,

`a=(100,000N-50,000N)/(5102.04kg)\approx9.8\text{ }m/s^2`

Hence, the elevator has an upward acceleration of 9.8 m/s² while braking.