Ten sense-making tasks on forces in balance. Explain your reasoning for every answer. The explanation counts as much as the answer.
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Each block hangs at rest, held up by two identical ropes. In each case the two ropes make the same angle with the ceiling. In B and C the ropes are vertical.
Rank the cases by the tension in one rope, 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 2.0 kg book rests on a level table. The two forces on the book are shown. Three students explain why these two forces are equal in size.
Ava: "The normal force and the weight are a Newton's 3rd law pair. That's why they're equal and opposite."
Ben: "They're equal because the book is in equilibrium. They're not a 3rd law pair: the partner of the Earth's pull on the book is the book's pull on the Earth."
Cam: "The normal force always equals the weight. That's just what a normal force is."
Which student(s), if any, do you agree with? Explain what is right or wrong about each statement. Then: if you press down on the book with a 5.0 N force, what is the normal force?
Back to topA box sits at rest on a rough 30° ramp. A student draws this free-body diagram. The student explains: "Gravity pulls down, the ramp pushes out, static friction holds it up the ramp, and $F_{parallel}$ is the force that tries to slide it down the ramp."
What, if anything, is wrong with this free-body diagram? If something is wrong, explain the error and describe the correct diagram. If nothing is wrong, explain why it is correct.
Back to topA crate of mass $m$ is at rest in each situation below. For each one, choose how the normal force exerted on the crate by the surface under it compares to $mg$:
A. greater than $mg$ B. equal to $mg$ C. less than $mg$ D. cannot be determined
| Situation (crate at rest) | Choice |
|---|---|
| (a) Sitting on a level floor, nothing else touching it | |
| (b) On a level floor, a person pushes on it at 30° below the horizontal | |
| (c) On a level floor, a person pulls on it with a rope at 30° above the horizontal | |
| (d) Sitting on a rough 20° ramp | |
| (e) On the floor of an elevator moving up at a constant 2 m/s | |
| (f) On a level floor with a second box stacked on top of it | |
| (g) On a level floor, with a rope pulling on it in a direction you are not told |
Explain the rule you used. How do you find the normal force when it is not equal to $mg$?
Back to topA light spring scale is connected by light strings over frictionless pulleys. In Setup 1 its left end is tied to a wall and a 1.0 kg block hangs from the right. In Setup 2 a 1.0 kg block hangs from each end. Everything is at rest.
For each quantity, state whether it is greater in Setup 1, greater in Setup 2, the same in both, or cannot be determined. Give values where you can.
| Quantity | Answer |
|---|---|
| (a) The scale reading | |
| (b) Tension in the string on the left side of the scale | |
| (c) Net force on the scale |
Explain each answer. What object plays the role of the second block in Setup 1?
Back to topA 2.0 kg block hangs from the middle of a light rope tied between two poles. The rope sags, making angle θ with the horizontal on each side. (The sag is exaggerated in the drawing.)
The two equations below are Newton's 2nd law (with $a = 0$) applied to one object:
$$(50\ \text{N})\cos37^\circ - f_s = 0$$
$$F_N + (50\ \text{N})\sin37^\circ - (20\ \text{kg})(10\ \text{m/s}^2) = 0$$
A small ring is held at rest by three ropes. The free-body diagram shows two of the forces. The third force is unknown.
A 6.0 kg sign hangs at rest from two ropes. Rope 1 makes 37° with the ceiling and Rope 2 makes 53° with the ceiling. Find the tension in each rope. Use $g = 10\ \text{m/s}^2$, $\sin37^\circ = \cos53^\circ = 0.60$, $\cos37^\circ = \sin53^\circ = 0.80$.
Student solution:
By symmetry, both ropes share the load equally: $T_1 = T_2 = T$.
Vertical: $T\sin37^\circ + T\sin53^\circ = mg$
$T(0.60 + 0.80) = (6.0\ \text{kg})(10\ \text{m/s}^2) = 60\ \text{N}$
$T = 42.9\ \text{N}$ in each rope
Identify the error in the solution. Explain the physics of why it's an error, then find the correct tensions. Which rope has the larger tension?
Back to topIn a tug-of-war, Pat and Sam each pull on the ends of a light rope with 200 N. Nobody moves.
Jordan writes: "The rope is pulled by both people, so the tension is $200\ \text{N} + 200\ \text{N} = 400\ \text{N}$."