An introduction to…Ticker-timers

1. Set up a ramp so that the angle above the horizontal can be changed. Place a bag or other soft object at the bottom of the ramp to catch the trolley.

2. Use a protractor to measure the angle of the ramp (θ) and record this value in a results table.

3. Connect a ticker-timer to a 50Hz AC supply and place at the top of the ramp.

4. Attach a length of ticker-tape to the back of a trolley and pass through the ticker-timer. Switch on the ticker-timer. Release the trolley and allow it to pull the tape through the timer. Switch off the ticker-timer.

5. Locate the starting point on the tape, where the dots are superimposed. Measure 0.50m along the tape and identify a 5-space length as shown on the diagram below. Measure the length (b) of these 5 spaces and record in your results table. 1. Knowing that, at 50Hz, these 5 spaces take 0.1s, determine the speed (v) at the 0.50m point. Calculate the square of the speed (v2) and the sine of the angle of the slope (Sinθ). Record the values in your table.

2. Change the angle of the slope and repeat the measurements. Repeat until you have at least 6 different angles with θ up to 20°.

3. Plot a graph of v2 (y-axis) against Sinθ (x-axis). Draw the best-fit straight line and determine the gradient and intercept of this line.

# Theory

As the trolley moves down the slope it loses gravitational potential energy, gains kinetic energy and there is work done against the force of friction (dissipating energy as heat). From the key idea of conservation of energy we have:

Loss of GPE = Gain of KE + work done by frictional force

For relatively slow speeds we can assume that air resistance is negligible. The frictional force will therefore be due to the drag of the ticker tape and the rolling resistance of the wheels, and be independent of speed — ie constant.

Rearranging and using conventional abbreviation letters we have: ½ mv2 = mgh — Fx v2 = 2gh — 2Fx/m The sine of the angle of the slope is h/x so: v2 = 2gx Sinθ – 2Fx/m

But x, the distance moved down the slope, has been set to be 0.50m and so: v2 = g Sinθ — F/m

Where g is the acceleration due to gravity, m is the mass of the trolley and F is the frictional force.