Beyond Force and Motion

Microcomputer-Based Lab

In this experiment you will investigate further the connection between the force applied to a cart and aspects of the cart’s motion along a track. This will require us to invent some new and useful concepts.

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 “Beyond Force and Motion”. This should start the software with three graphs displayed, one for force as a function of time, one for the area under the force vs. time graph as a function of time, and one for velocity as a function of time.

Investigating how the area under the force vs. time graph relates to the 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 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 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. Carefully position the cart at your origin. Release the cart from rest and then immediately hit the button. You won’t pick up the very start of the motion this way but that is perfectly fine. You should stop the cart by hand before it crashes into the pulley at the end of the track (or, even better, attach a stop to the track near the pulley). Examine the graphs carefully.

Remember Newton’s First Law, which states that an object will move with constant velocity unless acted upon by a net force. Combining this with Newton’s Second Law tells us that the longer we apply a net force to an object, the larger the effect on the object’s motion. That’s really what we’re getting at in this experiment – both the force applied and the time the force is applied have an impact on the motion of an object.

Question 1: As the cart moves along the track the force vs. time graph should be a horizontal line, so what should the total area under the force vs. time graph, as a function of time, look like? Is this what you observe?

Question 2: The shape of the area under the F-t graph should be similar to that of the velocity vs. time graph. Is it?

Question 3: Pick an arbitrary time t1 and find the value of the area under the force vs. time graph at this time. This value should be proportional to something on the velocity vs. time graph at the same time. What is this something? Check your answer by using a second time t2 that differs from t1 by a factor of 2.

Question 4: If you divide the area under the force vs. time graph by the “something” you found in question 3, what do you get? What units does this quantity have? What does this represent?

Question 5: Based on your analysis above, write out the equation below in a significantly simpler way:

The area under the force vs. time graph = ? * (something on the velocity vs. time graph)

The area under the force vs. time graph = _____ * _____

  1. Check your conclusions by repeating the experiment with a different mass hanging down from the pulley, and/or a different mass on the cart.

BONUS QUESTION 1: We have a one-word name for “the area under the force vs. time graph.” What is this name?

BONUS QUESTION 2: We have a name for what’s on the right-hand-side of the equation in question 5. What is this name?

1Beyond Force and Motion