Motion With Constant Acceleration



Force and Motion

Microcomputer-Based Lab

In this experiment you will investigate the connection between the force applied to a cart and the cart’s motion along a track.

Procedure

In this experiment you will use a cart with a force sensor mounted on it. The force sensor should have a hook on it, and tied to the hook is a string that passes over a pulley at one end of the track. You can hang various masses from the other end of the string, which will cause a force to be applied to the cart. The resulting motion of the cart will be measured with an ultrasonic motion sensor that you should mount at the end of the track that does not already have the pulley attached to it.

Make sure the cables from the two sensors, the force sensor and the motion sensor, are plugged into the LabPro interface, and make sure all other cables are removed. Double-click on the Logger Pro icon titled “Force and Motion”. This should start the software with four graphs displayed, one for position, one for velocity, one for acceleration, and one for force.

Investigating the connection between the net force and the motion

Prediction 1: In this experiment you will release the cart from rest, and it should gradually pick up speed because of the force applied to it by the tension in the string. Qualitatively, what do you expect the force graph to look like while the cart is in motion?

1. Determine the mass of the cart + force sensor combination.

2. Place the cart so it is at rest at some convenient point near the middle of the track, and do not yet place the string over the hook. This point will be your origin, but you need to tell the software that. To do that, keep your hands clear of the cart and click the [pic] button. You should zero all sensors, so you should hear the motion sensor clicking as it sends out pulses to determine where the cart is.

3. Now hit the [pic] button and move the cart back and forth. Which direction is the positive direction? It is probably most convenient to have the motion sensor treat the direction toward the pulley as positive for both motion and force. If one or both of these are currently negative you can reverse the positive and negative directions by going to the Setup menu and selecting Sensors. Choose the Details tab, select the appropriate sensor (either the force sensor or the motion sensor) and then press the Reverse Direction button

4. Now attach the string to the cart. Feed the string over the pulley and hang a mass from this end of the string. Choose a point to release the cart from rest. Hit the [pic] button and release the cart from rest a short time after you hear the motion sensor start to click. You should stop the cart by hand before it crashes into the pulley at the end of the track. Examine the graphs carefully.

Question 1: Can you tell from the graphs when you released the cart? If so, how can you tell?

Question 2: Now focus on the interval during which the cart is in motion. What does the force graph look like? How does it compare to what you predicted in Prediction 1 above?

Question 3: Do any of the three motion graphs (position vs. time, velocity vs. time, and acceleration vs. time) have the same general shape as the force vs. time graph? If so, which one? What does this tell you about the connection between the force and the motion?

Question 4: Using one of the motion graphs, determine the acceleration of the cart while the cart is in motion. How do you do this using the acceleration graph? How can you do this using the velocity graph? Find the acceleration from both the acceleration and velocity graphs and compare the two results. (Bonus question: how can you find the acceleration from the position graph?)

Question 5: From the force graph, determine the average force applied to the cart while it is in motion.

5. Without changing the mass of the cart or the mass hanging from the string, repeat the experiment a few times. Determine the acceleration of the cart each time from one of the motion graphs, and determine the average force applied each time.

Question 6: Comment on the consistency of your data.

6. Now repeat the experiment several times, each time changing the mass hanging from the string. For each trial determine the cart’s acceleration from one of the motion graphs, and determine the average force applied to the cart.

7. Construct a graph of the average force (on the y-axis) vs. the acceleration (on the x-axis).

Question 7: What relationship (e.g., linear, quadratic, etc.) do you observe between the force and the acceleration? If it is appropriate, determine the slope (including the units) of the best-fit line through your points. Does your slope correspond to any of the previous measurements you have done in the experiment?

Question 8: Summarize what you have learned from this experiment.

Question 9: Did anything in particular surprise you about this experiment? If so, what? Is there anything you would have liked to investigate further about the experiment? If so, what?

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