Question

Beryl (m=45kg) is standing in an elevator that is moving vertically upward at a speed of 3 m/s. 1.5 s later, the elevator and Beryl are moving vertically downward at a speed of 5 m/s. Beryl's feet remain in contact with the elevator's floor at all times, and that is Beryl's only point of contact with the elevator. (The y axis is vertical and positive upward)

What is the y-component of Bery;'s acceleration during that time interval?

What is the magnitude of Beryl's weight?

What is the magnitude of the normal force that the elevator exerts on Beryl during that time interval?

Answer 1

Solution: Mass of Beryl, m = 45 kg

Initial velocity of Beryl, u = 3 m/s               (vertical upward positive)

Final velocity of Beryl, v = - 5 m/s              (vertically downward velocity, negative)

Time interval of acceleration a is Δt = 1.5 s

The y component of Beryl’s acceleration “a” during the time interval of “Δt” can be found using following relation,

v = u + a*Δt

-5 m/s = (3 m/s) + a*(1.5 s)

a*(1.5 s) = - 5m/s – 3m/s

a*(1.5s) = - 8 m/s

a = (- 8 m/s)/(1.5s)

a = - 5.3333 m/s²

a = - 5.3                m/s²                                      (as per significant figure)

Negative sign indicates the downward acceleration.

The acceleration of Beryl is -5.3 m/s².

From the Newton’s second law, forces acting on Beryl are,

F_N – F_g = m*a

F_N = m*a + F_g

F_N = m*a + m*g

F_N = (a + g)*m                    ------------------------------------------------------------------------(1)

Where the F_N is the normal force on Beryl from the elevator floor, F_g = m*g weight of Beryl.

Now F_g = m*g is the gravitational force on Beryl which does not depend on the acceleration of the motion of Beryl, it is always constant. Thus,

F_g = m*g

F_g = (45 kg)*(9.81 m/s²)

F_g = 441.5 N

Thus the magnitude of the Beryl’s weight is 441.5 N.

The normal force on Beryl can be found using equation

F_N = (a + g)*m

F_N = (-5.3333 m/s² + 9.81 m/s²)*45 kg

F_N = 201.5 N

Thus the magnitude of normal force that elevator exerts on Beryl during that time interval is 201.5 N.