Half-Atwood Lab: Acceleration, Tension, and Friction

A cart on a table, a string over a pulley at the edge, and a mass hanging on the end. The simulation is on this page. Take g as 9.80 m/s squared, and take the two coefficients of friction as equal. Read every number exactly as the panel gives it.

Worth 50 points: 25 for completion, 25 for effort. Answers you type here are saved as you go, so you can close this and come back. Beside every part there is a button that opens Socrates on that part alone: he will not tell you what to write, he will ask you what you saw.

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1. Warm-up: release it and watch5 points

Set the cart to 2.00 kg, the hanging mass to 0.50 kg and the friction to zero. Press Release and watch the cart, the hanging mass and the panel.

Mass of the cart
Hanging mass
Friction under the cart

Draw a free-body diagram for the cart and one for the hanging mass, then write one sentence saying how you know the two objects have accelerations of the same size even though they move in different directions.5 pts

2. Change the hanging mass15 points

Leave the cart at 2.00 kg and the friction at zero for the whole of this part. Change the hanging mass only.

(a)Move the hanging mass slider from end to end. Say what happens to the acceleration and to the tension as the hanging mass grows, and compare the tension with the weight of the hanging mass at every setting you try.7 pts

(b)Fill the table in. Then explain why the tension is always smaller than the weight of the hanging mass while the system is accelerating, and say what would have to be true for the two to be equal.8 pts

Hanging mass	Acceleration (m/s²)	Tension (N)	Weight of the hanging mass (N)
0.20 kg
0.40 kg
0.60 kg
1.00 kg

3. Change the cart instead15 points

Now leave the hanging mass at 0.50 kg and the friction at zero, and change the cart.

(a)Move the cart slider from end to end. Say what happens to the acceleration as the cart gets heavier, and say what number the acceleration climbs toward as the cart is made lighter and lighter. Name the situation that number belongs to.7 pts

(b)Fill the table in. The tension goes the other way from the acceleration. Say what value the tension climbs toward as the cart is made heavier and heavier, and explain why it can never quite reach it.8 pts

Mass of the cart	Acceleration (m/s²)	Tension (N)
0.50 kg
1.00 kg
2.00 kg
3.00 kg

4. Put friction under the cart15 points

Set the cart back to 2.00 kg and the hanging mass to 0.50 kg, and use the friction slider.

(a)Raise the friction a step at a time, pressing Release each time, until the cart stops moving at all. Say the setting at which it stops, and name the two numbers in the panel that decide whether it moves or not.7 pts

(b)Fill the table in. Then look at the row where nothing moves and say what the tension is in that row, why it is that value, and what has become of the friction force there.8 pts

Friction setting	Largest friction the table can give (N)	Acceleration (m/s²)	Tension (N)
0
0.10
0.20
0.30