Calculating Apparent Weight on a Rotor Ride

AI Thread Summary
The discussion centers on calculating the apparent weight of a 30-kg child on a rotor ride, with specific parameters such as a 3 m radius and a rotation speed of 0.4 revolutions per second. The initial calculation determined the child's velocity as 7.54 m/s and suggested that the apparent weight equals the normal force (FN) at 568.5 N. However, the correct approach incorporates both the normal force and gravitational force, leading to an apparent weight of 640 N when calculated using the resultant force formula. The importance of considering friction and the normal force in relation to the child’s apparent weight is emphasized, clarifying the role of these forces in the scenario. Understanding these dynamics is crucial for accurately determining apparent weight in rotational motion contexts.
LesterTU
Messages
6
Reaction score
0

Homework Statement


A 30-kg child is on a rotor ride at a carnival. The radius of the rotor is 3 m and it completes 0.4 revolutions in one second. The coefficient of static friction is 0.6. What is the magnitude of the child's apparent weight?

rotor1.png

Homework Equations


ΣFx : FN = mv2/r
ΣFy : Ff = Fg

The Attempt at a Solution


First I need to find v:
0.4 revolutions per second is equivalent to one revolution per 2.5 s, so T = 2.5 s.
v = 2πr / T => v = 7.54 m/s.

Since the apparent weight is the magnitude of the resultant force exerted on a body by a supporting surface, the way I see it FN is the only force that fits this description so I figured
apparent weight = FN = mv2/r = 568.5 N.

However the solution given by the author says that
apparent weight = (FN2 + Fg2)1/2 = 640 N.

I've been trying to understand why mg plays a role in the child's apparent weight but I don't see how in this case
 
Physics news on Phys.org
Hello and welcome to PF!

Are you sure that FN is the only force exerted on the person by the wall? Consider the forces shown in your figure.
 
Thanks!

I guess the friction applies in this case but for some reason because of its direct relationship with the normal force I didn't consider it. It makes a lot of sense though now that I think about it
 
OK, good.
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top