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Motion Exp. No.1 - Position-time Graph and Velocity Aims: 1. To record the motion of a dynamics cart by ticker-timer tape. 2. Determine the velocity of the cart. Theory: A ticker-timer has a frequency of 50 Hz, with a time interval of 0.02 seconds per dot. Attached to a moving cart, the ticker-timer tape will display how far the cart has moved in the 0.02 seconds between dots. Method: Set up a ticker-timer and attach the tape to a dynamics trolley. Push the trolley across the floor, activating the ticker-timer after the cart has left your hand. Recover the tape and analyse the motion, recording the distance the cart travelled every 0.10 seconds [ ie. 5 time intervals ]. Analysis: Tabulate the distances travelled (cm) in each 0.1 second time interval and hence the total distance travelled (cm) vs. time (s). Draw a position-time graph of the motion. From this graph, estimate the average velocity of the cart, in cms-1 and ms-1. Questions: 1. Why is the frequency of the ticker-timer 50 Hz? 2. How is the time between dots calculated? 3. Why was the ticker-timer started after you had pushed the cart? 4. What’s the difference between speed and velocity? 5. What shape ( if any ) did your position-time graph display? 6. Was the velocity of your cart fairly constant? [ explain ] 7. How is velocity determined from a position-time graph? 8. How else could you estimate the average velocity from these results? 9. What force would be involved in slowing the cart after it left your hand? Motion Exp. No.2 - Velocity-time Graph and Acceleration Aims: 1. To record the motion of a dynamics cart moving down a slope. 2. Estimate the acceleration of the cart. Theory: The average velocity travelled by the cart every 0.1 seconds can be calculated, these values can then be plotted against time [ in the middle of each time interval ] to establish a velocity-time graph. Method: Set up a ticker-timer and attach the tape to a dynamics trolley at the top of a slope. Activate the ticker-timer and immediately release the trolley. Recover the tape and analyse the motion. Analysis: Tabulate the distances travelled (cm) and the average velocity of the cart (cms-1) in each 0.1 second time interval. Draw a velocity-time graph of the motion, with the average velocity plotted against the midpoint of each time interval [ ie. 0.05 s, 0.15 s, 0.25 s etc.]. From this graph, estimate the average acceleration of the cart, in cms-2 and ms-2. Questions: 1. Why was the cart released as the ticker-timer was activated? 2. What is acceleration? 3. What shape ( if any ) did your velocity-time graph display? 4. What does this indicate about the motion of the cart? 5. How is acceleration estimated from a velocity-time graph? 6. How else could you estimate the acceleration from these results? 7. What forces contributed to the acceleration of the cart? 8. Sketch how a position-time graph of these results might appear. Motion Exp. No.3 – Equation of Motion Aim: To record the motion of a dynamics cart moving down a slope by ticker-timer tape and use the results to verify the equation of motion… x = ut + ½ at2 Theory: For an object travelling at a constant acceleration in a straight line, its displacement, x is given by … x = ut + ½ at2 , where u is it’s initial velocity, a the acceleration and t the time taken. Method: Set up a ticker-timer and attach the tape to a dynamics cart at the top of a sloping ramp. Mark the position of the front wheel of the cart. Activate the ticker-timer and immediately release the trolley. Stop the ticker timer immediately it reaches the bottom of the ramp. Use a tape measure to record the distance from initial front wheel of the trolley to the end of the ramp. Recover the tape and analyse the motion. Analysis: Tabulate the distances travelled (cm) and the average velocity of the cart (cms-1) in each 0.1 second time interval. Use these results to estimate the average acceleration of the cart, in cms-2 [ either by drawing a velocitytime graph or by noting the change in velocity between 2 separated time intervals ]. Use the equation … x = ut + ½ at2 to estimate the displacement the cart. Compare this estimate to the measured distance the cart moved. Questions: 1. What’s the difference between displacement and distance? 2. How did the calculated displacement compare to the measured distance? 3. What factors may be operating to invalidate the equations of motion? 4. Explain how you could perform this experiment to verify… v2 = u2 + 2ax. Motion Exp. No.4 – Acceleration due to Gravity Aim: To use a ticker-timer analysis of a falling weight to estimate the acceleration due to gravity, g. Theory: Any object, regardless of size, in free fall [ only force acting is gravity ] will accelerate downwards at 9.80 ms-2, which is the acceleration due to gravity at the Earth’s surface. Method: Set up a ticker-timer above and clear of the lab bench. Attach ticker tape to a 500 g weight and hold it just below the timer and directly above a sand filled catch tray. Activate the timer and immediately drop the weight. Recover the tape and analyse the motion. Analysis: Tabulate the distances fallen (m) and the average velocity of the weight (ms-1) in each 0.1 second time interval. Draw a velocity–time graph of the falling weight. Use these results to estimate the acceleration of the cart, in ms-2. Questions: 1. Did your results show that acceleration of the falling weight is constant? 2. Compare your value of “g” with what was expected, giving reasons for any discrepancy between your result and the accepted value. 3. Suggest how this experiment could be improved to provide a very good experimental value for “g”. 4. If the 500 g weight used in your experiment was replaced with a 1 kg weight, would it have fallen faster? 5. The gravitational field strength at the Earth’s surface is 9.80 Nkg-1. The gravitational field strength of the moon is 1.6 Nkg-1. What is the acceleration due to gravity on the moon? Motion Exp. No.5 – Acceleration due to Gravity The purpose of this activity is for your team to produce an experimental value for “g” that more closely approximates the accepted value of 9.80 ms-2 for Melbourne. You will need to read the information below, then design and set up your experiment, obtain results and then calculate your value of “g”. You should then evaluate your experiment and suggest improvements. When a pendulum swings with a small amplitude, the mass on the end [the pendulum bob] fairly closely approximates simple harmonic motion. The period of a pendulum [ie. time for it to swing from one extreme to the other and back again] depends on the length of the pendulum [from the axis of rotation to the centre of mass of the pendulum bob] and the acceleration due to gravity, g. This dependence can be expressed mathematically as … T = 2[L/g] T = period (s) L = length (m) g = acceleration (ms-2) Motion Exp. No.6 – Force on an inclined plane Aim: To demonstrate that for an object free to move on a slope inclined at o to the horizontal, the force pulling it down the slope is given by the component of its weight acting down the slope. Theory: An object on a slope is subjected to a force due to the component of it’s weight acting down the slope = Fds = mgsin … where m = mass [kg], g = 9.8 [ms-2] and = angle of the incline. Method: Set up and measure the angle of inclination of a sloping ramp. Measure the mass of an unloaded dynamics cart. Use a spring balance to measure the force acting on the unloaded dynamics cart positioned on the ramp. Repeat this using 2 different loads on the cart. Change the angle of inclination to 2 other values and repeat the previous measurements. Tabulate all the results [ you should have 9 sets of data ]. Analysis: Calculate the force down the slope for each set of data using Fds = mgsin and record the results in a table like the one shown below … cart mass (kg) slope angle (o) measured force (N) Fds = mgsin (N) Questions: 1. How well did your calculated force approximate the measured force? 2. How is the weight of an object calculated? 3. Apart from the weight force acting on the cart, what other real forces would effect the motion of the cart on the slope? 4. Sketch a force diagram of the cart, showing the nature and direction of these forces. Motion Exp. No.7 – Hookes Law Aims: 1. To establish the force-extension graph of a spring 2. Determine the force constant [k] of the spring [in Nm-1] Theory: A spring obeys Hookes law if its extension is directly related to the force extending it, resulting in a linear force-extension graph. The gradient of a linear force-extension graph is the force constant, K. The energy stored in an extended spring is … Es = ½Kx2. Method: Hang a light spring from a retort stand and measure its un-extended length. Add 50 g masses and record the extension of the spring [ up to 400 g in mass ]. Tabulate results. Analysis: Calculate the weight force [ W = mg ] applied to the spring and record the results in a table like the one shown below … force applied [N] 0.48 0.96 extension [m] Draw a force-extension graph and determine the gradient, which is the force constant K, in Nm-1. Questions: 1. Did the spring obey Hookes law? How could you tell? 2. What was the force constant of your spring? 3. Use your graph to find how far the spring would extend if a 165 g cricket ball was attached { Hint: balls weight force, W = mg } 4. Assuming Hookes law applies, calculate the energy stored in your spring when it is extended by 8.0 cm { Hint: Es = ½Kx2 } Motion Exp. No.8 – Momentum and Energy Changes Aim: To demonstrate whether kinetic energy and momentum are conserved when objects collide. Theory: Momentum is the product of mass and velocity [ p = mv ] and is a vector quantity measured in kgms-1. Kinetic energy is the energy possessed by a moving object [ Ek = ½mv2 ] and is a scalar quantity measured in J. When objects collide, the total momentum and kinetic energy before the collision can be compared to those after the collision. Method: Record the mass of two different gliders. Attach Velcro to the ends of the gliders so they will lock together on impact. Place the larger glider at rest in the centre of the air track and gently push the larger glider towards the smaller one. Use stopwatches to measure the time taken by the first cart, and then the joined carts, to cover 50.0 cm of track. Analysis: Calculate the velocity of the larger glider before collision and the velocity of the combined gliders after collision [ v = 0.50/t ]. Calculate the kinetic energy and momentum of the large glider before it collides and the kinetic energy and momentum of the combined gliders after collision. Questions: 1. What was the total momentum and kinetic energy of the system before the gliders collided? { Hint: it’s the p and Ek of the large glider } 2. What was the total momentum and kinetic energy of the system after the collision? { Hint: it’s the p and Ek of the combined gliders } 3. Which of the 2 quantities was “better conserved” during the collision? [ use experimental data to support your answer ]. 4. If kinetic energy or momentum are not conserved in a collision, where do they go?