Investigating a pendulum

Transcription

1 P3 3.6 Student practical sheet Investigating a pendulum The period of a pendulum is the time it takes to complete one swing. Different pendulums have different periods, so what determines the period of a pendulum? Aim To investigate the factors that may affect the period of a pendulum. Equipment clamp and stand G-clamp metre rule stop clock string optional: light gate and datalogger stacking masses Safety Use the G-clamp to clamp the stand to the ench so that it cannot fall over. What you need to do 1 Set up a pendulum using the clamp and stand. For now the length and mass you use do not matter. Use the G-clamp to fasten the ottom of the stand to the edge of the ench so that it does not fall over when the pendulum swings. 2 The period of a pendulum is the time for one complete swing. Swing the pendulum and measure its period. Repeat this five times and note how reliale your results are. 3 Plan an investigation to find out which factors affect the period of a pendulum. Your plan needs to explain the following. Which factors you will investigate. How you will investigate each of these factors. How you will you make your tests fair. What values you will use for your independent variales. How you will you measure the period of the pendulum to otain accurate results. How you will make sure your test is safe. 4 Show your plan to your teacher efore you start. Using the evidence 1 Present your results for each investigation as a tale and a graph. (5 marks) 2 How does each factor affect the period of the pendulum? Explain how you otain your conclusion from the graphs. (2 marks) 3 If there does appear to e a relationship etween one of your variales and the period, is the relationship proportional? Explain your answer. (1 mark) Sheet 1 of 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 325

2 P3 3.6 Student practical sheet Evaluation 4 How reliale are your results? How do you know? (2 marks) Extension 5 The following equation can e used to calculate the period of a pendulum for small amplitudes: T = 2π l/g, where g is the acceleration due to gravity. What does this equation tell you aout the factors that affect the period? (2 marks) 6 Calculate the period for some of the pendulums you tested in the investigation (use g = 9.81 m/s 2 ). (4 marks) 7 How do your calculated values compare to your experimental results? Suggest reasons for any differences. (2 marks) Sheet 2 of Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.

3 P3 3.6d Student worksheet Swinging questions Figure 1 1 Explain the difference etween the period of a pendulum and its frequency. (2 marks) 2 The adult in the drawing pushes the ay on swing A every five seconds. a What is the period of the swing? (1 mark) What is its frequency? (2 marks) 3 What is the frequency of swing B? Explain your answer. (2 marks) 4 Look at the teenagers on swings C, D and E. a Explain how the frequency of swings C, D and E will compare to each other. (3 marks) Explain how their frequencies will compare to the ay swings. (2 marks) 5 Figure 2 shows a pirate ship ride at a fairground. How does the period of this ride compare to the period of playground swings? Explain your answer. (2 marks) Figure 2 Extension 6 The period of a pendulum can e worked out using the formula T = 2π l/g, where T is the period in seconds, l is the length of the pendulum (in metres) and g is the acceleration due to gravity in m/s 2 (use 9.81 m/s 2 ). Use this formula and the drawing of the pirate ship to estimate the period of the pirate ship when it is swinging. (3 marks) Sheet 1 of 1 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 327

4 P3 3.6e Student worksheet Simple harmonic motion A pendulum is an example of a system with periodic motion. Many periodic systems undergo simple harmonic motion. The characteristics of simple harmonic motion include: an oscillation aout an equilirium position the motion follows a sinusoidal pattern (a graph of displacement against time looks like the graph of the sine function) the force on the ody is proportional to the displacement and points in the opposite direction. These characteristics can e illustrated y thinking aout a mass attached to a spring. When the mass is at rest and the spring is not stretched, there are no horizontal forces on the mass. This is the equilirium position for the mass. (Figure 1) Figure 1 If the mass is pulled to one side the spring is stretched. The force from the spring acts in the opposite direction to the displacement. As the mass is pulled further away the force from the spring increases. (Figure 2) Figure 2 Simple harmonic motion occurs when the mass is released. (Figure 3) When the mass is released, the force from the spring will accelerate it ack towards its original position. When it reaches its original position the spring will e unstretched and so it will not e exerting a force on the mass. The mass is moving with its maximum velocity. The mass will continue to move and will start to compress the spring. As it moves further it compresses the spring more and the force from the spring increases. This force is in the opposite direction to its movement and so the mass decelerates. Figure 3 Sheet 1 of Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free.

5 P3 3.6e Student worksheet 1 Continue the sequence of drawings in Figure 3 y showing what happens to the velocity of the mass and the forces on it as it returns to the position from which it was released. (4 marks) The first graph in Figure 4 shows how the displacement varies. The displacement is greatest when the mass is released, at point A. At point B it has returned to its starting position, and at C it is at its greatest displacement in the opposite direction. At D it is passing ack through its starting position again. The shape of the line is a sine wave. The second graph shows some information aout how the velocity varies. In the conventions used here, velocity is negative when the mass is moving to the left. The velocity is at its most negative (or positive) when the mass is moving through its original position. Figure 4 2 Copy the graphs and complete the graphs for velocity and force. The questions and hints elow will help you to do this. (2 marks) When the displacement is greatest, what is the velocity of the mass? When is the velocity the most positive (or negative)? Is the force on the mass greatest when the displacement is large or small? When the mass is displaced to the right the force acts to the left, so when the displacement is positive the direction of the force is negative. 3 a What is the 'equilirium position' for a pendulum? (1 mark) c d e What is the force that returns a pendulum to its equilirium position if the o is displaced? (1 mark) At which point(s) in a pendulum's swing is this force greatest? (1 mark) At which point(s) is this force least? Explain your answer. (2 marks) At which point(s) in a pendulum's swing is it moving fastest? (1 mark) 4 Sketch a set of graphs, similar to the ones aove, showing how the displacement, velocity and force vary with time for a swinging pendulum. (3 marks) Sheet 2 of 2 Pearson Education Ltd Copying permitted for purchasing institution only. This material is not copyright free. 329