# Test of mv²/R on a turntable

##### Demonstration

An alternative method of investigating centripetal force quantitatively.

#### Apparatus and materials

Turntable

Truck attachments (see Technical notes and the diagram below)

Stopwatch or stopclock

Fractional horsepower motor (with gear box)

LV variable power supply

chemical balance with a sensitivity of no less than 0.1 g

Forcemeter, reading up to 10 N

#### Health & Safety and Technical notes

Do not increase the rotational speed of the turntable too much; otherwise there is a risk of objects 'flying off' and causing injury.

Fix the truck attachment securely to the top of the turntable, as illustrated below. The section of model railway track extends radially and the toy truck is pulled towards the centre by a spiral spring.

The turntable has to be rotated steadily. This can be done by hand, but it is more convenient to drive the turntable using the fractional horsepower motor and the gear box which can be attached to it. The speed of rotation is then conveniently controlled by adjusting the power supplied to the motor.

The position of the truck for various orbital speeds can be marked with a flag, or an electric contact can be arranged to light a lamp when the truck 'makes a circuit' at a particular radius. In some models, the end plate is moveable so that different radii can be selected and the truck always hits the end plate.

The experiment is sensitive to the levelling of the turntable.

It may be necessary to increase the mass of the truck for satisfactory results.

See the following website for a supplier of Fractional horsepower motors.

#### Procedure

a Gradually increase the track's speed of rotation until the truck just reaches the stop at the end of the track. Time 50 revolutions of the turntable and calculate the time for one revolution.

b Measure the radius of the circle described by the rotating truck, R, and calculate the speed of the truck in its orbit, v

c Find the mass of the truck, m, using the balance.

d With the turntable at rest, use a forcemeter to measure the force, F, required to extend the spring by the same amount as it does when the truck hits the end stop.

e Compare this actual force with the theoretical value of the centripetal force, mv²/R .

#### Teaching notes

1 This experiment assumes that students have already been taught that centripetal acceleration,a = v²/R. They are now finding out whether the formula for centripetal acceleration, F = ma = mv²/R, is reasonable. F is the real force (the force of the spring pulling on the rotating truck) and mv²/Ris the predicted centripetal force.

2 You could increase the mass of the truck by loading it with one or more lead plates, repeating the demonstration and calculation for each mass.