Challenge: To analyze all forces in a system to achieve a constant target velocity.
Parameters: You will tie two adjustable masses to a 500g mass in a 188g dynamics cart. The masses will be hanging over either end of the table over pulleys. After a push from you, the cart and passenger will move at a constant velocity of 25.00 cm/s for a minimum of 60 cm. The cart must have a “flag” from Mr. J taped to it for my photogate measurements. In your journal you must show all your analysis of motion and forces.
Scoring: You will be scored on the ability of your system to move at a constant target velocity of 25.00 cm/s. I will measure your cart’s velocity using photo gates. Your score will be based primarily on how much your velocity changes, and secondarily on how close you are to the target average velocity. You will be given three tries in a maximum of five minutes of testing. Your best try will be scored.
Score = | average velocity - 25.00 cm/s | + 5 (∆v)
average velocity is the simple average of the two velocity measurements, while ∆v is the absolute value of the difference between the two velocity measurements made during the 60 cm run of your cart.
Your rank will be based on your score, lowest score being awarded highest rank.
Physics: Your system will accelerate according to Newton’s Second Law if the forces on it are unbalanced. You will need to push the cart to accelerate the system from rest to 25 cm/s velocity. You are the unbalanced force! Once you let go you want the remaining forces to be BALANCED so that the system does not speed up or slow down. There are many forces on your system, including friction, all of which can be determined by using Newton’s laws of motion. Free-body diagrams are very helpful in determining forces. The average velocity can be determined simply by timing the 60 cm run, but the instantaneous velocity must be analyzed from a video record of position and time data.
Extensions: As an extension, try to determine the relationship between the hanging masses and friction forces.
Help/Hints: You will find position and time data from video analysis. (use lots of light, and slow motion is not required) Google sheets can generate position-time and velocity time graphs, which will tell you if you have achieved the target velocity and how constant the velocity is.
Quiz Topics: Kinematics of constant velocity in one dimension
Newton’s Laws of Motion in one dimension
Free-body diagram