Ten sense-making tasks on Newton's laws. Explain your reasoning for every answer. The explanation counts as much as the answer.
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Each block sits on a frictionless horizontal surface. The only horizontal forces acting on each block are shown.
Rank the blocks by the magnitude of their acceleration, 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 ball is thrown straight up. It rises, stops for an instant at its highest point, and falls back down. Ignore air resistance. Three students discuss the net force on the ball at the very top.
Ava: "At the top the ball stops, so the net force on it must be zero at that instant."
Ben: "The net force at the top is just the ball's weight, pointing down. It's the same the whole way up and the whole way down."
Cam: "On the way up there's an upward force from the throw that keeps getting smaller. At the top it finally equals gravity, so the ball stops."
Which student(s), if any, do you agree with? Explain what is right or wrong about each statement.
Back to topA box is given a quick shove up a rough incline. After the hand lets go, the box keeps sliding up the incline while slowing down. A student draws this free-body diagram for the box after it leaves the hand:
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 student of mass $m$ stands on a bathroom scale in an elevator. For each situation, choose what the scale reads:
A. greater than $mg$ B. equal to $mg$ C. less than $mg$ D. cannot be determined
| Situation | Choice |
|---|---|
| (a) Moving up at constant speed | |
| (b) Moving up and speeding up | |
| (c) Moving up and slowing down | |
| (d) Moving down and speeding up | |
| (e) Moving down and slowing down | |
| (f) Momentarily at rest at the top of its trip, about to start down |
Explain the rule you used. What do the situations with the same answer have in common?
Back to topAn 80 kg adult and a 40 kg child stand at rest on frictionless ice, facing each other. They put their hands together and push off.
For each quantity, state whether it is greater for the adult, greater for the child, or the same for both. If it's different, give the ratio.
| Quantity (during the push) | Answer |
|---|---|
| (a) Magnitude of the force each one feels from the other | |
| (b) Magnitude of each one's acceleration | |
| (c) The time interval each one feels a force | |
| (d) Speed of each one right after they separate |
Explain each answer. Would anything change if only the adult pushed and the child kept their arms relaxed?
Back to topA cart of mass $M$ sits on a frictionless table. A light string runs over a frictionless pulley. In Setup 1, a block of mass $m$ hangs from the string. In Setup 2, the block is removed and a hand pulls down on the string with a constant force equal to $mg$.
The equation below is Newton's 2nd law applied to one object in some physical situation:
$$(40\ \text{N})\cos 30^\circ \;-\; 0.25\Big[(8.0\ \text{kg})(10\ \text{m/s}^2) - (40\ \text{N})\sin 30^\circ\Big] = (8.0\ \text{kg})\,a$$
The graph shows the velocity of a cart of mass $m$ moving along a straight track.
A 10 kg block is pulled across a rough floor ($\mu_k = 0.30$) by a rope with a tension of 50 N at 37° above the horizontal. Use $g = 10\ \text{m/s}^2$, $\sin37^\circ = 0.60$, $\cos37^\circ = 0.80$.
Student solution:
$F_N = mg = (10\ \text{kg})(10\ \text{m/s}^2) = 100\ \text{N}$
$f_k = \mu_k F_N = (0.30)(100\ \text{N}) = 30\ \text{N}$
$T_x = (50\ \text{N})\cos37^\circ = 40\ \text{N}$
$a = \dfrac{40\ \text{N} - 30\ \text{N}}{10\ \text{kg}} = 1.0\ \text{m/s}^2$
Identify the error in the solution. Explain the physics of why it's an error, then find the correct acceleration.
Back to topA 5.0 kg box sits at rest on a ramp inclined at 20°. The coefficient of static friction is $\mu_s = 0.60$.
Jordan writes: $f_s = \mu_s F_N = (0.60)(5.0\ \text{kg})(10\ \text{m/s}^2)\cos20^\circ = 28.2\ \text{N}$, so the friction force on the box is 28.2 N up the ramp.