# Further test of mv²/R

##### Class practical

This is a modification of the experiment Experimental test of F = mv²/R.

#### Apparatus and materials

For each pair of students

Metal ball, 50-100 g (or rubber bung)

Thin string or nylon cord, length about 1.5 m

Rod, length 20 cm, diameter 1 cm

Curtain ring

Long spring

Short, weak spring, made from think Manganin wire wound onto a pencil

Forcemeter, 0-10 N or masses

Balance to find mass or metal ball (or rubber bung)

#### Health & Safety and Technical notes

Ensure there is sufficient area around each student when whirling. Keep away from windows, etc.

Securely attach rubber bungs to the string. Ensure the string is held tightly as it is whirled around the head.

Observers should wear safety spectacles.

The curtain ring is held in place on the wooden handle with two washers and nails. It is free to rotate around the handle. Note: File off the sharp point of the nail.

Attaching the long spring: Using a light string, tie one end of the long spring to the curtain ring, at a distance of 10 cm. Tie the other end of the long spring to a metal ball, at a distance of about 30 cm.

Attaching the short spring: Using similar string, fix one end of the small spring to the curtain ring, at a distance of 2.5 cm. Feed string tied to the other end of the small spring through the long spring to prevent the thread from getting tangled and tie it to the mass end of the long spring. Finally, fix a short piece of string to either end of the small spring so that it cannot stretch to more than 7.5 cm.

#### Procedure

a Gently swing the mass in a horizontal circle above your head, gradually increasing the rotation speed so that the long spring stretches and the small spring is stretched almost to its full extent. Your partner now times 50 full rotations.

b Measure the radius of the orbit (the length from the ring to the ball) by placing the device flat on a bench with the mass pulled outwards so that the springs are stretched by the same amount as in step a

c Use the data collected in steps a and b to calculate the orbital speed, v

d Hang the spring vertically and load it with masses (or pull it with the forcemeter) so that the springs are stretched by the same amount as in step a. Record the force F needed to do this.

e Measure the mass, and calculate the theoretical centripetal force mv2/R. Compare with the actual force F

#### Teaching notes

1 The long spring serves both to produce a variable force - so that the orbit is stable - and to measure that force. The tension in the long string is measured by inserting a piece of string through it which is connected to a small spring - to show when the spring is stretched a standard amount, and to prevent over stretching of the spring. The small spring is only used as a signal and does not contribute significantly to the central force.

When the device is whirled faster and faster the long spring stretches more and more until it begins to pull its main safe-guarding thread taut. The weak spring remains unstretched with its thread loose, until the safeguarding thread is just taut. Then, at that speed, the weak spring acts as a signal.

2 The tension in the long spring is the centripetal force, F. The predicted size of the force required for an orbit is mv2/R. The point of the experiment is to compare the predicted force to the spring tension providing the centripetal force.