Unit 3 check

Unit 3 check: Work, Energy, and Power

10 questions from 5 lessons in Unit 3. Answer each one, and if you miss, follow the link back to where it is taught, then try again. Your score counts first tries.

Question 1 · from 3.1 · Calculate

A 2.0 kg cart moves along a straight track; take right as positive. Its position is $x (t) = 3 t^{2} - t^{3}$ , with $x$ in meters and $t$ in seconds. What is the cart's kinetic energy at $t = 1.0$ s?

Your answer J

Question 2 · from 3.2 · Calculate

A launcher's arm pushes a puck along a straight, level track in the $+ x$ direction. While they touch, the arm's force on the puck is $F_{x} (x) = 12 - 3 x^{2}$ , with $F_{x}$ in newtons and $x$ in meters. The force falls to zero at $x = 2.0$ m, where the puck leaves the arm. How much work does the arm do on the puck from $x = 0$ to $x = 2.0$ m?

Your answer J

Question 3 · from 3.3 · Calculate

A small magnet moves along a straight track, the $x$ -axis, near magnets fixed beside the track. The potential energy of the system is $U (x) = 4 x^{3} - 6 x$ , with $U$ in joules and $x$ in meters. Take the direction of increasing $x$ as positive. What is the $x$ -component of the conservative force on the small magnet at $x = 1.5$ m?

Your answer N

Question 4 · from 3.4 · Calculate

A cable lifts a 10 kg box straight up from rest. Its pull on the box is $F (y) = 120 - 10 y$ , with $F$ in newtons and $y$ in meters measured upward from the starting point. Take the box and Earth as the system, use $g = 10$ m/s² and ignore air resistance. How fast is the box moving when $y = 2.0$ m?

Your answer m/s

Setup for question 5

On paper. A rope parallel to a ramp drags a crate up the ramp at a steady speed, and kinetic friction acts on the crate. Draw the crate as a dot, with an arrow for each force on it (the rope's pull, gravity, the normal force and friction) and a separate arrow for its velocity. Next to each force, write whether it delivers positive, negative or zero power to the crate, and why, from the angle between that force and the velocity. Then check your work: the rope's pull lies along the velocity, so its power is positive; the normal force is perpendicular to the velocity, so its power is zero; friction points opposite the velocity, so its power is negative; and gravity points more than 90° from the velocity, which runs up the slope, so its power is negative too. At a steady speed the four powers add to zero.

Question 5 · from 3.5 · Calculate

A winch is switched on, and the power it delivers to a crate rises steadily: $P (t) = 60 t$ , with $P$ in watts and $t$ in seconds, for $0 \leq t \leq 5.0$ s. How much work does the winch do on the crate in the first 5.0 s?

Your answer J

Question 6 · from 3.1 · Sort it

Each card describes the velocity of the same 2.0 kg puck sliding on level ice, with east as $+ x$ and north as $+ y$ . Tap a card, then choose the puck's kinetic energy.

9.0 J

16 J

25 J

Question 7 · from 3.2 · Calculate

A 0.20 kg hockey puck slides east across rough, level ice at 8.0 m/s. The ice exerts a kinetic friction force of 0.30 N on it, and no other force has a part along its motion. How fast is the puck moving after it slides 15 m?

Your answer m/s

Question 8 · from 3.3 · Fill the statement

A particle moves along the $x$ -axis as part of a system whose potential energy is $U (x) = x^{3} - 12 x$ , with $U$ in joules and $x$ in meters. The particle has equilibrium positions at $x = + 2$ m and $x = - 2$ m. The $+ x$ direction points to the right.

At $x = + 2$ m, $U$ has a local . A small nudge to the right of $+ 2$ m gives a force to the , so $+ 2$ m is a equilibrium position. A small nudge to the right of $- 2$ m gives a force to the .

Setup for question 9

On paper. A 0.50 kg cart is released from rest 0.80 m above the bottom of a track with negligible friction. Use $g = 10$ m/s² and take $U_{g} = 0$ at the bottom. Make a table of the cart-Earth system's $U_{g}$ , $K$ and $E_{mech}$ at heights of 0.80, 0.60, 0.40, 0.20 and 0 m. Plot $U_{g}$ and $K$ against height on one set of axes, with scales and units on both. Then write a procedure to test whether the mechanical energy of a real cart-Earth system stays constant: what you would measure, with what equipment, how you would compare the results with your table, and what result would show that it does not stay constant. There is nothing to submit here.

Question 9 · from 3.4 · Rank it

Three identical balls are thrown, and air resistance is negligible; use $g = 10$ m/s². Ball A is thrown straight up at 10 m/s from the edge of a roof 20 m above the ground and misses the roof on the way down. Ball B is thrown horizontally at 10 m/s from the same roof. Ball C is thrown straight down at 15 m/s from a balcony 10 m above the ground. Rank the balls by their speed just before they hit the ground.

Greatest first

Give each one a place, 1 for first. Give two the same place if they are equal.

Ball A
Ball B
Ball C

Your ranking: none yet

Setup for question 10

A winch at the end of a level track winds in a cable that pulls a cart along the track, starting from rest at $t = 0$ ; take the cart's direction of travel as positive. The cable stays parallel to the track. A sensor in the winch records the power the cable delivers to the cart, and a speed sensor records the cart's speed. Some of the readings:

Winch and speed sensor readings
$t$ (s)	$P$ (W)	$v$ (m/s)
0	0	0
1.0	296	1.98
2.0	604	4.03
3.0	897	5.97
4.0	1203	8.02

Question 10 · from 3.5 · Calculate

Estimate the work the cable does on the cart from $t = 0$ to $t = 4.0$ s, as the area under the power readings found with the trapezoid rule, one trapezoid for each 1.0 s step.

Your answer J

0 of 10 answered.