[Grade 12 Physics] Gravitational/circular motion #2

In summary: The problem says "apparent weight" to imply ##F_n##.Similar situation described here for an object speeding on Earth's surface. Complicated a bit by Earth's rotation.
  • #1
hobbes1235
13
0
Homework Statement
A certain asteroid has a radius of 7.0x10^3 m and a mass of 5.0x10^15 kg. How fast would a cyclist have to travel on the surface of this asteroid in order for her apparent weight to be one-fifth of her weight when stationary.
Relevant Equations
Fcentripetal = ma
a = v^2 / r
Fg = GMm / r^2

Potential Energy = -GMm / r
Kinetic Energy = 0.5(mV^2)
Total Energy (Ek + Ep) = -0.5(GMm) / r

g = Fg / m
Diagram for question 2:

rotated2-jpg.jpg


Please check if my work is correct.
Main equation: Fc = Fg - Fn
Fn = Fg - Fc
I assume that: Fn = Fg when stationary
Fg = mg
I divide by 5 because the apparent weight must be one fifth of her weight when stationary
Fg = mg / 5
Fn = Fg
Fn = mg / 5
Now to substitute back into the equation Fn = Fg - Fc
Fn / m = g - V^2 / r

Fn(r) / m = g(r) - V^2

mgr / 5m = gr - V^2

-(gr / 5) + gr = V^2

V = 6.17 m/s^2
 
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  • #2
Your work looks correct to me. However, I found the following lines a little confusing:

hobbes1235 said:
I assume that: Fn = Fg when stationary
Fg = mg
I divide by 5 because the apparent weight must be one fifth of her weight when stationary
Fg = mg / 5
Fn = Fg
Fn = mg / 5

You got to the correct result: Fn = mg/5. But I didn't quite follow your logic.

The apparent weight is given by the normal force Fn. And you want this to be 1/5 of the actual weight. Hence,
Fn = mg/5. Maybe that's what you were thinking?
 
  • #3
I actually didn't know that the apparent weight was Fn but it turned out to be correct. What even is "apparent weight" I thought it was the weight when moving.
 
  • #4
hobbes1235 said:
I actually didn't know that the apparent weight was Fn but it turned out to be correct. What even is "apparent weight" I thought it was the weight when moving.
Your phrase "weight when moving" is vague. Many would say that it is still the attraction due to gravity, which is not changed by the motion. The problem says "apparent weight" to imply ##F_n##.
 
  • #6
hobbes1235 said:
I actually didn't know that the apparent weight was Fn but it turned out to be correct. What even is "apparent weight" I thought it was the weight when moving.
Weight is the force with the which the Earth, or the asteroid in this case, attracts the object. Apparent weight is the force that a bathroom scale would measure. Contrary to popular belief, a bathroom scale measures the normal force exerted on its surface, not the weight of an object placed on it. When you push on a bathroom scale with your hand, it does not display your weight, does it?

Thus, if you stand on a bathroom scale in a moving elevator, it will display more than your weight if the elevator is accelerating up, less than your weight if accelerating down and your weight if moving at constant speed up or down or is at rest. The same situation applies here except that the normal force is different from the weight not because the mass is accelerating in a straight line but because it is going around in a circular path while maintaining contact with the surface.
 

Related to [Grade 12 Physics] Gravitational/circular motion #2

1. What is the difference between uniform circular motion and non-uniform circular motion?

Uniform circular motion is when an object moves in a circular path at a constant speed, while non-uniform circular motion is when the speed of the object changes as it moves along the circular path.

2. How is centripetal force related to circular motion?

Centripetal force is the force that acts towards the center of a circular path and keeps an object moving in that path. It is essential for circular motion as it maintains the direction of the object's velocity.

3. How does the radius of the circular path affect the speed of an object in circular motion?

The speed of an object in circular motion is directly proportional to the radius of the circular path. This means that as the radius increases, the speed also increases, and vice versa.

4. Can an object in circular motion have a constant speed and a changing velocity?

Yes, an object in circular motion can have a constant speed but a changing velocity. This is because velocity is a vector quantity that takes into account both speed and direction. In circular motion, the direction is constantly changing, even if the speed remains constant.

5. How does gravity affect circular motion?

Gravity is the force that attracts two objects towards each other. In circular motion, gravity acts as the centripetal force that keeps an object moving in a circular path around a larger object, such as a planet or a star.

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