Calculating Gravitational Force on a Point Mass in a Semicircular Rod

In summary, the conversation discusses the gravitational force exerted by a bent uniform rod on a point mass located at the center of curvature. The solution involves breaking the rod into small bits of mass and integrating over the masses to find the total y component of the force. This can be simplified by converting to an integral over an angle.
  • #1
pete06
2
0
A uniform rod of mass M = 20kg and length L = 5m is bent into a semicircle. What is the gravitational force exerted by the rod on a point mass m = 0.1 kg located at the center of curvature of the circular arc?
 
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  • #2
I have assumed that this must be solved using the summation of all points on the rod since each exerts its own force on the point mass. Assuming that to be true, I figured that the x components all cancel each other out, leaving only the y components. But now, I don't know how to solve this?
 
  • #3
You are on the right track. You have the symmetry figured out. Break the rod up into bits of mass dm and write the y component of the force related to each bit of mass. Add all the y components (integrate over the masses). This is most easily done by converting to an integral over an angle.
 

Related to Calculating Gravitational Force on a Point Mass in a Semicircular Rod

What is gravitational force?

Gravitational force is a natural phenomenon of attraction between two objects with mass. It is the force that keeps planets in orbit around the sun and holds objects to the surface of the Earth.

How is gravitational force measured?

Gravitational force is measured in units of Newtons (N). The force between two objects can be calculated using the equation F = G * (m1 * m2)/d^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between them.

What factors affect the strength of gravitational force?

The strength of gravitational force is affected by the masses of the objects and the distance between them. The larger the masses of the objects and the closer they are to each other, the stronger the gravitational force between them will be.

How does gravitational force differ from other forces?

Gravitational force is a long-range force that acts between objects with mass, while other forces such as electromagnetic force and strong and weak nuclear forces act on a smaller scale between particles. Gravitational force is also always attractive, while other forces can be either attractive or repulsive.

Can gravitational force be shielded or cancelled out?

No, gravitational force cannot be shielded or cancelled out. It is a fundamental force of nature that cannot be eliminated or blocked. However, its effects can be counteracted by other forces, such as the upward force of a chair supporting your weight against the Earth's gravitational force.

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