# Physics

posted by .

There is a horizontal rod of length L and mass M. A point mass m is vertically above the rod at a vertical distance L/4 and horizontal distance L/3 from one end of the rod.Using The Riemann sum Integral,find the magnitude and direction of the gravitational force exerted on the point mass by the rod.

• Physics -

Write the expression for the vertical and horizontal components of the gravoty force. It will require an integration along the length of the rod.

The vertical force component is
G*m*(M/L)*dx*(L/4)/[(L/4)^2 + x^2]^3/2
integrate that from x=0 to x = L
The messy looking denominator is the cube of the distance between mass m and dx. You need a cube instead of a square becasue you need to include a cosine term for the vertical component. For the horizontal force, you will have a different integral beasue you need a sine term.

Doing this with Riemann sums is rather messay and I will leave that you you or another teacher

## Similar Questions

1. ### AP Physics

A uniform thin rod of length 0.3m and mass 3.5kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 3g bullet traveling in the horizontal plane of the rod is fired into one end of the …
2. ### Math

There is a horizontal rod of length L and mass M. A point mass m is vertically above the rod at a vertical distance L/4 and horizontal distance L/3 from one end of the rod.Using The Riemann sum Integral,find the magnitude and direction …
3. ### physics

a 51.0 kg uniform square sign, of edge L = 2.00 m, is hung from a horizontal rod of length dh = 3.00 m and negligible mass. A cable is attached to the end of the rod and to a point on the wall at distance dv = 4.00 m above the point …
4. ### Physics

A 2.5 m rod of mass M= 4. kg is attached to a pivot .8m from the left end so that it can rotate vertically. At the left end of the rod is a small object with mass m=1.5kg. A spring with a spring constant k=90N/m is attached to the …
5. ### Physics

A nonuniform 2.0-kg rod is 2.0 m long. The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod. The moment of inertia of the rod about this axis is 4.0 kg m2. The …
6. ### physics

A uniform rod of mass M = 0.245kg and length L = 0.49m stands vertically on a horizontal table. It is released from rest to fall. (a) Calculate the angular speed of the rod, the vertical acceleration of the moving end of the rod, and …
7. ### physics

A thin non-uniform rod of length L=2.00 m and mass M=9.00 kg is free to pivot about an axis at one end. The CM of the rod is at a distance d=1.30 m from that end as illustrated below. The rod's moment of inertia about an axis through …
8. ### physics

A uniform thin rod of length 0.55 m and mass 5.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is a rest when a 3.0-g bullet traveling in the horizontal plane of the rod is fired into one end …
9. ### Physics

A mass of 100g is attached to one end of a massless rod, 10cm in length, which is pivoted about the opposite end. The rod is held vertical, with the mass at the top, and released. The rod swings. A. What is the speed of the mass at …
10. ### Physics

In the figure, a thin uniform rod of mass m = 3.05 kg and length L = 1.11 m rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at a distance d = 0.201 m from the end of the rod. The …

More Similar Questions