Question

A 520 kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 200 m. (a) What is the centripetal acceleration of the child? m/s Direction (b) What force (magnitude and direction) does the seat evert on the child at the lowest point of the ride? magnitude direction . (from upward) (c) What force does the seat exert on the child at the highest point of the ride? magnitude direction • (from upward) (d) What force does the seat exert on the child when the child is halfway between the top and bottom? magnitude direction Enter a number differs from the correct answer by more than 100%. (from upward)

Answer 1

Given is:-

Mass of the child m = 52 kg

Diameter of the wheel D = 20m

Thus radius of the wheel r = 10m

Angular speed   or   $w = \frac{4 \times 2 \pi rad}{60s } = 0.419 rad/s$

Now,

part - a

The centripetal acceleration is

by plugging all the values we get

which gives us

and the direction towards the centerr

ae 1.756m/s

Part - b

The force exerted by the seat on the child at the lowest point is given by

F = F_c + mg

F_c is the centripetal force = ma_c g is the acceleration due to gravity = 9.8 m/s²

F = m(ac+g)

F = (52 kg)(1.756 m/s²+9.8 m/s²)

which gives us

$\boxed{F = 600.912 N}$ and the direction is upward or 0 degree from upward

Part - c

The force exerted by the seat on the child at the highest point is given by

F = -F_c + mg

F = m(-a_c+g)

F = (52 kg)(-1.756 m/s²+9.8 m/s²)

$\boxed{F = 418.288 N}$ and the direction is upward or 0 degree from upward

Part - d

The half way between the top and bottom:

In theis situation, the centripetal force F_c (towards the center) on the child and the weight mg (downwards) are perpendicular to each other

The magnitude of the net force is

F = √[F_c²+ (mg)²]

$F = \sqrt{(F_c)^2 + (mg)^2}$

by plugging the values we get

$F = \sqrt{(52kg \times 1.756m/s^2)^2 + (52 kg \times 9.8m/s^2)^2}$

which gives us

$\boxed{F = 517.716 N}$

and the direction is

$\theta = tan^{-1}(\frac{52 \times 9.8}{52 \times 1.756})$

which gives us

$\theta =169.84 ^\circ \text{ from the upward direction}$