Ten sense-making tasks on torque and rotational equilibrium. Explain your reasoning for every answer. The explanation counts as much as the answer.
showmethephysics.com
Each picture is a top view of an identical 1.0 m wide door hinged at its left edge (black dot). One force acts on each door in the plane of the picture. The distance $r$ from the hinge to where the force is applied is given. (Arrows are not drawn to scale.)
Rank the doors by the magnitude of the torque about the hinge, from greatest to least. If any are equal, show the tie. If the ranking cannot be determined, say so.
Greatest 1 ____ 2 ____ 3 ____ 4 ____ 5 ____ 6 ____ Least
Explain your reasoning.
Back to topA 30 kg child sits 2.0 m from the pivot of a seesaw. A 60 kg parent sits 1.0 m from the pivot on the other side. The seesaw is horizontal and balanced. Ignore the mass of the board.
Four students explain why the seesaw balances:
Ava: "The parent pushes down harder, so the parent's side should really go down. It only stays level because the board is stiff."
Ben: "It balances because the child's torque about the pivot and the parent's torque about the pivot are equal in size and opposite in direction. The forces don't have to be equal."
Cam: "It balances because the forces on the two sides are equal. The parent's weight is spread over less of the board, so it acts like the same force as the child's."
Dee: "The pivot doesn't exert any torque about itself, but it still pushes up on the board with a force of 900 N."
Which student(s), if any, do you agree with? Explain what is right or wrong about each statement.
Back to topA uniform 4.0 m plank weighing 200 N rests on two sawhorses, one at each end. A 400 N painter stands 1.0 m from the left end. A student draws this force diagram for the plank:
Student's note: "Total weight is 600 N and there are two sawhorses, so each one pushes up with 300 N. The forces add to zero, so the plank is in equilibrium."
What, if anything, is wrong with this diagram and reasoning? If something is wrong, explain the error and find the correct support forces. If nothing is wrong, explain why it is correct.
Back to topA light meter stick is held at rest, horizontal, on a frictionless pivot at its center. Two forces are then applied as described in each row, and the stick is released. All "up" and "down" forces are vertical.
For each case, choose what the stick does right after release:
A. starts rotating clockwise B. starts rotating counterclockwise C. stays at rest (no rotation) D. cannot be determined
| Case | Choice |
|---|---|
| (a) 10 N down at 20 cm left; 5 N down at 40 cm right | |
| (b) 10 N down at 30 cm left; 10 N up at 30 cm right | |
| (c) 10 N down at 25 cm left; 20 N down at 10 cm right | |
| (d) 8 N down at 50 cm right; 8 N pulling horizontally (along the stick) at 50 cm left | |
| (e) 12 N down applied directly at the pivot; 6 N down at 20 cm right | |
| (f) 10 N down somewhere on the left; 10 N down somewhere on the right |
Explain the rule you used. Which cases surprised you?
Back to topTwo identical 120 N signs hang from the ends of identical light horizontal rods. Each rod is attached to a wall by a hinge and held up by a cable tied to the end of the rod. In Setup A the cable makes a 30° angle with the rod. In Setup B the cable makes a 60° angle with the rod.
For each quantity, state whether it is greater in A, greater in B, or the same in both. If different, give the ratio.
| Quantity | Answer |
|---|---|
| (a) Torque exerted by the sign's weight about the hinge | |
| (b) Torque exerted by the cable about the hinge | |
| (c) Tension in the cable | |
| (d) Horizontal force the hinge exerts on the rod |
Explain each answer. Then calculate the cable tension in each setup.
Back to topA 0.90 kg baseball bat balances on your finger at the point shown. You saw the bat in two at exactly that balance point.
The equation below is a torque equation for an object in static equilibrium, with torques taken about a hinge:
$$T\sin 30^\circ\,(2.0\ \text{m}) \;-\; (50\ \text{N})(1.0\ \text{m}) \;-\; (100\ \text{N})(1.5\ \text{m}) = 0$$
A uniform 1.0 kg meter stick balances, at rest, on a pivot at the 30 cm mark. A block of unknown mass $m$ hangs from the 10 cm mark.
A uniform 6.0 m plank weighing 300 N rests on support A (1.0 m from the left end) and support B (5.0 m from the left end). A 600 N person stands 4.0 m from the left end.
Student solution: Take torques about support A.
$F_B(5.0\ \text{m}) = (300\ \text{N})(3.0\ \text{m}) + (600\ \text{N})(4.0\ \text{m})$
$F_B = \dfrac{900\ \text{N·m} + 2400\ \text{N·m}}{5.0\ \text{m}} = 660\ \text{N}$
$F_A = 900\ \text{N} - 660\ \text{N} = 240\ \text{N}$
Identify the error in the solution. Explain the physics of why it's an error, then find the correct support forces.
Back to topA door is stuck in its frame. A student pushes on it with a 40 N force, perpendicular to the door, 0.80 m from the hinge. The door does not move at all. (Top view.)
Morgan writes: "$\tau = rF = (0.80\ \text{m})(40\ \text{N}) = 32\ \text{N·m}$. Since newton-meters are the same as joules, I did 32 J of work on the door."