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

ANSWER

9.8 m/s² up

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,

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

Solving the net-force equation for a,

$a=\frac{F-F_g}{m}$

Replace the known values and solve,

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

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