Name Date Lab: Impulse-Momentum Theorem Introduction: In this lab you will determine the change in momentum of a cart colliding with a spring. Then you will use a force sensor to find the force and collision time of a cart crashing into two springs of different stiffness. Activity 1: Finding Initial Momentum For this activity you will place the cart at the top of the aluminum track and allow the cart to roll to the bottom and bounce off the rigid (stiff) spring. You will determine the velocity of the cart the instant before it collides with the spring. The cart starts at the top of the track at rest The cart is just about to collide with the spring I. Determine which string is most rigid (stiff) and screw it into the force sensor at the bottom of the track. II. Place the cart at the very top of the track and measure the distance the front of the cart will travel until it hits the spring. III. Next you will determine the time it takes for the cart to travel down the track to the spring using a stopwatch. Repeat this three times and find the average time it takes the cart to reach the spring. IV. Now answer the questions to find the velocity of the cart just before it hits the spring. 1) Distance the cart will travel in meters: 2) Times for the cart to reach the bottom of the incline in seconds: Times (s) 1) 2) 3) Average time in seconds: 3) Draw a picture of this situation and label all six variables that are involved in constant acceleration problems. 4) To determine the velocity of the cart just before it hits the spring, which kinematic equation should be used? (Use the Kinematic Equation Reference Sheet provided at the lab table to assist you.) 5) Use the equation you chose for question (4) and find the velocity of the cart when it reaches the spring. Express your answer in (m/s). (Assume that velocity down the slope is negative.) 6) The mass of the cart is 0.25 kg. Find the momentum of the cart just before it hits the spring. We will call this the initial momentum. Record you answer below. (The initial momentum should be negative.) Initial Momentum:
Activity 2: Finding Final Momentum For this activity you will place the cart at the top of the aluminum track and allow the cart to roll to the bottom and bounce off the rigid (stiff) spring. You will determine the velocity of the cart the instant after the cart leaves the spring moving back up the track. The cart starts at the bottom of the track moving up the ramp The cart has moved up the ramp and slows to 0 m/s I. Place the cart at the very top of the track allow the cart to go down the track and hit the spring. II. As soon as the cart hits the spring start the stop watch and determine the time it takes for the cart to move up the track to the turnaround point. III. Measure the distance from the spring to the turnaround point. IV. Repeat the three times and find the average time it takes the cart to reach the turnaround point from the spring and the average distance the cart travels up the ramp from the spring to the turnaround point. V. Now answer the questions to find the velocity of the cart just after it leaves the spring moving back up the track. 7) Distance the cart will travel in meters: Distances (m) 1) 2) 3) Average distance (m): 8) Times for the cart to reach the bottom of the incline in seconds: Times (s) 1) 2) 3) Average Time (s): 9) Draw a picture of this situation and label all six variables that are involved in constant acceleration problems. 10) To determine the velocity of the cart just after it leaves the spring moving up the ramp, which kinematic equation should be used? (Use the Kinematic Equation Reference Sheet provided at the lab table to assist you.) 11) Use the equation you chose for question (10) and find the velocity of the cart when it leaves the spring. Express your answer in (m/s). (Assume that velocity up the slope is positive.) 12) The mass of the cart is 0.25 kg. Find the momentum of the cart just after it leaves the spring. We will call this the final momentum. Record you answer below. (The final momentum should be positive.) Final Momentum: 13) Find the change in velocity and the change in momentum of the cart from just before it hits the spring to just after it leaves the spring. Change in Velocity in (m/s): Change in Momentum in (kg m/s):
Force Force Activity 3: Examining Impulse Now that you have determined the change in Momentum of the cart you will now examine the impulse applied to the cart by the rigid (stiff) spring and a less rigid spring. Note: both springs will cause the same change in momentum you found in part (13). Finding impulse applied to the cart by the rigid (stiff) spring I. You will be using the GLX and the motion sensor to determine the average applied force and time the spring applies the impulse to the cart. Press the play button on the GLX to start collecting data on the GLX and then Zero out the force sensor by pressing Zero button on the top of the force sensor. Press the play button on the GLX to stop collecting data. II. Place the cart at the top of the incline, as you have done before. Release the cart and press the play button on the GLX. When the cart collides with the spring the force-time graph on the GLX will spike as shown to the right. Press the Time play button to stop collecting data. Press F1 on the GLX to autoscale the graph. III. You will now move and rescale the graph to better the section that recorded the data in which the cart collided with the spring. Press F2 twice until Move appears above F2 on the GLX. Move the spike on the graph to the left by pressing the left arrow button. IV. Press F2 until you see Scale above F2 on the GLX. Stretch the spike on the graph to the right by pressing the right arrow button. Your graph should look something like the one to the right. Time V. Next you will find the time interval that of collision with cart and the rigid spring. Do this by pressing F3 on the GLX and arrow and down to Delta Tool and press the check button. Use the arrow and place the first cursor at the bottom left part of the graph where the graph just starts to rise from the x-axis. Press F3 and arrow down to Swap Cursor and arrow the second cursor to the bottom right part of the graphs where the graph falls back to the x-axis. The change in time (the time the collision occurred) will be displayed just above the x-axis highlighted in black. Record the collision time below. VI. Now you will find the average applied force acting on the cart from the spring by pressing F3 and arrows get down to Statistics. The cursors should already be in the correct positions from when you found the change in time. Record the average force below. Finding impulse applied to the cart by the less rigid spring I. Replace the rigid spring with the less rigid spring. II. Repeat the experiment and find the change in time (collision time) and force acting on the cart by the less rigid spring. Record these values in the next section. 14) Rigid (Stiff) Spring Collision with Cart Data Collison Time (s) Average Force (N) Calculated Impulse (kg m/s) 15) Less Rigid Spring Collision with Cart Data Collison Time (s) Average Force (N) Calculated Impulse (kg m/s) 16) The impulse of both the rigid and less rigid springs acting on the cart should be the same. The less rigid spring applies less average force on the cart than the rigid spring. Explain how each spring can apply the same impulse yet the less rigid spring applies less average force on the cart.
Activity 4: Changing the Mass of the Cart For this activity you will place the rigid (stiff) spring back on the force sensor and add mass to the cart and use the GLX to find the resulting change in time and average force acting on the cart. Use the method you learned in Activity 3 to find the change in time and average force for each run. First run the experiment with just the cart (250 g) then add 250 g and perform the experiment again. Repeat 3 more times. Record you data in the table below. Total mass (kg) 0.250 0.500 0.750 1.000 1.250 Collision Time (s) Average Force (N) Impulse (kg m/s) The Impulse-Momentum is: J = m v. Where J is impulse, m is mass, and v is change in velocity. Make a graph of impulse (y-axis) vs. mass (x-axis) the result will be a line with the slope equal to the change in velocity of the cart from the instant just before it hits the spring to just after it leaves the spring. Label axes and draw a best-fit line using a straight edge. 17) Find the slope of the impulse-mass graph and record your answer below. (Include proper units) 18) The slope of the graph should equal the change in velocity of the cart from the instant just before it hits the spring to just after it leaves the spring. Compare the slope you found in part (17) to the change in velocity you found in part (13) by finding the percent difference. Use the change in velocity from part (13) as the expected value and the slope as the measured value. Remember: % Difference = Measured value Expected value Expected value 100
Impulse-Momentum Theorem Use the following situation to make the graph and answer questions (1-4) The force required to break a large egg from the grocery store is determined to be around 25 N. A group of students perform a series of experiments on an egg by dropping the egg onto a 2 inch foam mat from different heights. A force sensor is placed under the foam mat to determine the average force applied to the egg and collision time when the egg hits the foam to come to a rest. The students record the height the egg was dropped, the average force, and the collision time in a table. See the table below. Height Dropped (m) Average Force (N) Collision Time (s) Impulse (kg m/s) Change in Velocity (m/s) 0.20 2.3 0.050 2.0 0.40 4.6 0.035 2.8 0.60 7.0 0.030 3.4 0.80 9.1 0.025 4.0 1.00 11.5 0.023 4.4 1) Calculate the impulses and record them in the proper places in the table above. 2) The Impulse-Momentum is: J = m v. Where J is impulse, m is mass, and v is change in velocity. Make a graph of impulse (y-axis) vs. Change in Velocity (x-axis) the result will be a line with the slope equal to the mass of the egg. Label axes and draw a best-fit line using a straight edge. 3) Determine the slope of the Impulse-Change in Velocity graph to determine the mass of the egg. Record the mass in grams below. Mass of egg in grams:
4) A baseball with a mass of 0.145 kg is traveling 42 m/s the instant before it is hit by a bat. The bat is in contact with the ball for 7.0 x 10-4 seconds and has a final velocity of -65 m/s. a) Draw an impulse-momentum bar graph of this situation. b) Find the value of the impulse that was given to the baseball (magnitude only). c) Find the magnitude of the force acting on the baseball during its collision with the bat. 5) A car with a mass of 1,125 kg is traveling at a speed of 35 m/s when it crashes into a barrier. A force of 41,000 N is applied to the car by the barrier to stop the car completely a) Draw an impulse-momentum bar graph of this situation. b) Find the value of the impulse that was given to the car (magnitude only). c) Find the collision time of the car during its collision with the barrier. 6) A person with a mass of 75 kg jumps from a table and lands on the floor. The force applied to the person s feet by the floor is 4,500 N for a time of 0.25 seconds. a) Draw an impulse-momentum bar graph of this situation. b) Find the value of the impulse that was given to the person (magnitude only). c) Find the initial velocity of the person the instant before hitting the floor.