Gravitational field Questions

In summary: Running/walking means placing feet in front of each other alternately in a manner that avoids falling over. The difference between them is that running swings the legs faster than their natural period.
  • #1
Bashyboy
1,421
5

Homework Statement


Assume you are agile enough to run across a horizontal surface at 8.50 m/s, independently of the value of the gravitational field. What would be (a) the radius and (b) the mass of an airless spherical asteroid of uniform density 1.10 310 3kg/m3 on which you could launch yourself into orbit by running? (c) What would be your period? (d) Would your running significantly affect the rotation of
the asteroid? Explain.


Homework Equations





The Attempt at a Solution


I have a few conceptual questions that pertain to this problem. I have a belief that the force with which the person running exerts on the surface is equal and opposite to the gravitational force that the asteroid provides, and is the reason why this person is running at a constant speed. However, I am not sure of why I have this suspicion. Also, I know this is a very elementary question, but how is it possible for a person to run if the ground provides and equal and opposite force to the force that the person exerts on the surface with there foot?
 
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  • #2
Hi Bashyboy! :smile:
Bashyboy said:
I have a belief that the force with which the person running exerts on the surface is equal and opposite to the gravitational force that the asteroid provides …

Why? One is horizontal and the other is vertical, so why should they cancel? :confused:
… how is it possible for a person to run if the ground provides and equal and opposite force to the force that the person exerts on the surface with there foot?

The only (horizontal) force on the person is the force from the ground.

Start again. For parts (a) (b) and (c), you can pretend the speed is supplied by a rocket.​
 
  • #3
Bashyboy said:
the force with which the person running exerts on the surface is equal and opposite to the gravitational force that the asteroid provides
If they are equal and opposite, how are you able to keep running around the curve of the surface (instead of traveling in a straight line)?
tiny-tim said:
One is horizontal and the other is vertical, so why should they cancel? :confused:
Since speed is constant, both forces are vertical.
 
  • #4
I think I am experiencing a little confusion myself. How is the force with which the runner pushes against the ground vertical?
 
  • #5
Bashyboy said:
I think I am experiencing a little confusion myself. How is the force with which the runner pushes against the ground vertical?

the push force (using friction) is horizontal

i think haruspex is thinking of the normal reaction force
 
  • #6
Okay, so the person pushes against the ground, and the ground provides friction that propels the person forward because there is no other force that keeps the person from not moving, right?
 
  • #7
no other horizontal force, right :smile:
 
  • #8
Hmm, well what does the speed being constant have to do with their being a normal force every instant that the person plants their foot on the ground and the gravitational force, the two vertical forces haruspex is speaking of.
 
  • #9
tiny-tim said:
the push force (using friction) is horizontal
tiny-tim, I think you are misreading the question.
A steady speed is attained by some means. There is now no horizontal force; the tangential speed is constant. The only acceleration (while staying on the surface) is vertical (centripetal). There is no friction, no drag. The question is, what is the size of the sphere if 8.5m/s is just enough to start losing contact with the surface?
Bashyboy, it will only complicate matters unnecessarily if you consider actual bipedal motion. Simpler to treat it as bicycling.
 
  • #10
uhh??

the question was …
Bashyboy said:
… how is it possible for a person to run if the ground provides and equal and opposite force to the force that the person exerts on the surface with there foot?

if you're not exerting a horizontal force, you're not running
tiny-tim said:
The only (horizontal) force on the person is the force from the ground.

… you can pretend the speed is supplied by a rocket.
 
  • #11
tiny-tim said:
if you're not exerting a horizontal force, you're not running
That is not true. If there is no drag and you're not gaining or losing speed or changing direction then there cannot be a horizontal force. Your feet are hitting the ground merely to provide a vertical force. In practice, there will be small variations to the horizontal velocity of your mass centre, but they will average out to zero.
 
  • #12
haruspex said:
If there is no drag … Your feet are hitting the ground merely to provide a vertical force.

exactly … not running! :smile:

(more sort of rolling)
 
  • #13
tiny-tim said:
exactly … not running! :smile:

(more sort of rolling)
No, doesn't have to be rolling, though that would be a less confusing model with which to discuss the intended question.
Running/walking means placing feet in front of each other alternately in a manner that avoids falling over. The difference between them is that running swings the legs faster than their natural period. It normally entails a propulsive force because of resistance, but if running down a slight incline it is obvious that a propulsive force provided by friction on the ground need not be present. If it weren't for the inherent instability of our upright posture we could run some distance across ice, somewhat like a bouncing ball.
But let's get back to the OP. It is quite clear that the question is really asking what the radius of the asteroid is if 8.5m/s is just fast enough for a surface-level orbit.
 
  • #14
I still don't quite understand how the person is able to move forward--or is it the planet that is rolling backwards?
 
  • #15
if a stationary person wants to start moving forward, he uses his leg muscles to rotate at the knee, which makes the foot want to move backward relative to the body

since gravity results in a normal force between him and the planet, this movement produces a horizontal friction force

so instead of the body rotating slightly (but not moving forward), the whole body moves forard and the planet very slightly moves backward :smile:
 
  • #16
tiny-tim said:
if a stationary person wants to start moving forward, he uses his leg muscles to rotate at the knee, which makes the foot want to move backward relative to the body

since gravity results in a normal force between him and the planet, this movement produces a horizontal friction force

so instead of the body rotating slightly (but not moving forward), the whole body moves forard and the planet very slightly moves backward :smile:
Agreed. But for the purposes of the question we need not be concerned with how the speed of 8.5m/s was achieved. All that matters is that if it were just slightly faster you would take off.
 

1. What is a gravitational field?

A gravitational field is a region in space where objects with mass experience a force of attraction towards each other. This force is known as gravity, and it is responsible for keeping planets in orbit around the sun and objects on Earth from floating off into space.

2. How is the strength of a gravitational field measured?

The strength of a gravitational field is measured by its gravitational field strength, which is a measure of the force per unit mass that a test object would experience at a given point in the field. It is often represented by the symbol g and is measured in units of meters per second squared (m/s²).

3. How does the mass and distance of objects affect the strength of a gravitational field?

The strength of a gravitational field is directly proportional to the mass of the objects involved and inversely proportional to the square of the distance between them. This means that as the mass of an object increases, the strength of its gravitational field also increases. Similarly, as the distance between two objects increases, the strength of their gravitational field decreases.

4. What is the difference between a gravitational field and a gravitational force?

A gravitational field is a region in space where objects with mass experience a force of attraction towards each other. On the other hand, a gravitational force is the actual force of attraction between two objects with mass. The strength of the gravitational field determines the strength of the gravitational force.

5. How does the concept of gravitational field relate to Einstein's theory of general relativity?

Einstein's theory of general relativity describes how gravity is not just a force between masses, but is actually a curvature of space and time caused by the presence of mass and energy. This curvature is what creates the gravitational field and explains the motions of objects in space without the need for a force of gravity.

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