## Determination of an Unknown Mass By Equilibrium of Forces

1 x tall retort stand and boss; 1 x short retort stand, clamp and boss; 1 x rod; 1 x free-running pulley wheel; 1 x plumb-line; 1 x 100cm length of string; 1 x 10cm length of string; 1 x mass labelled 'X', 1 x metre rule; 1 x half-metre rule; 1 x felt-tipped pen; 1 x set square; 4 x 100g masses on a holder

Procedure:

1. Clamp the rod to a stand at about 60cm above the bench, and clamp the pulley wheel to a stand about 35cm above the bench. Set the stands about 70cm apart.

2. Tie the longer piece of string to the rod and pass this string over the pulley wheel. Tie the 100g mass holder to the end of this string. This is the initial value of

3. Tie the shorter piece of string from massto the other string at point O. See diagram below..

4. Adjust the position of the pulley wheel and the stand which holds it until, with the strings coplanar and the system in equilibrium,the string between the pulley wheel and O is horizontal, as shown in the diagram.

5. Make a mark on the string between O and the rod, about 2 cm away from the rod.

This mark is at distance k from point O. Measure and record distance k.

6. Measure and record the horizontal distance d between O and the mark made on the string.

You will need to use the set-square and plumb-line to do this.

7. Repeat for four larger values of m. Each time readjusting the position of the pulley wheel and the stand which holds it until the string between O and the pulley wheel is horizontal.

Measure the corresponding distance d between O and the mark already made on the string.

8. Calculate d2; m2; d- 2 (i.e. 1 divided by d 2); & m- 2 (1 divided by m2)

9. Tabulate all your measurements and calculations.

10. Plot a graph of(- axis) against(- axis). It should be a straight line graph.

11. Determine the gradient,of this graph.

12. Evaluate the square-root of this gradient,and then multiply your answer by the distance

Your answer should be equal to the mass of

13. Answer the following questions:

(a) Explain how you established that the system was in equilibrium.

(b) Explain how you measured the horizontal distance