Unit 7 check

Unit 7 check: Oscillations

10 questions from 5 lessons in Unit 7. 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 7.1 · Fill the statement

A toy hanging from a springy cord is pulled down once and let go. Left alone, it bobs through 12 full up-and-down cycles in 30 s.

Motion that repeats in equal time intervals is called motion. The toy's period is . Whether its motion is also simple harmonic depends on .

Question 2 · from 7.2 · Calculate

A 2.0 kg block on a level, frictionless table is attached to a horizontal ideal spring with spring constant 50 N/m. The block is pulled 0.10 m to the right of its equilibrium position, with right as positive, and released. What is the period of its oscillation?

Your answer s

Question 3 · from 7.3 · Decide and justify

A glider on a horizontal spring has position $x (t) = 0.12 \sin (π t)$ , with $x$ in meters, $t$ in seconds and the angle in radians. Its equilibrium position is $x = 0$ , and right is positive. At $t = 0.50$ s, what is the size of the glider's acceleration?

Which reason supports your answer?

Question 4 · from 7.4 · Rank it

Three blocks oscillate on horizontal springs on frictionless surfaces. Oscillator P has $k = 100$ N/m, amplitude 0.10 m and a 1.0 kg block. Oscillator Q has $k = 25$ N/m, amplitude 0.20 m and a 4.0 kg block. Oscillator R has $k = 50$ N/m, amplitude 0.20 m and a 1.0 kg block. Rank the oscillators by the total energy of each block and spring system.

Greatest first

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

Oscillator P
Oscillator Q
Oscillator R

Your ranking: none yet

Setup for question 5

On paper. Draw any rigid object you like hanging from a pivot, turned counterclockwise through a small angle $θ$ from equilibrium. Mark the pivot, the center of mass, the distance $d$ between them and the gravitational force exerted on the object at its center of mass, and write the torque that force exerts about the pivot, with its sign. Then describe how you would measure the period of small swings with a stopwatch so that your reaction time matters as little as possible. There is nothing to submit here.

Question 5 · from 7.5 · Calculate

A 2.0 kg steel bracket of irregular shape hangs from a horizontal pivot pin and swings in a vertical plane. Its center of mass is 0.25 m from the pin. For small swings, a photogate measures a period of 1.40 s. What is the bracket's rotational inertia about the pin?

Your answer kg·m²

Question 6 · from 7.1 · Calculate

A glider on a level, frictionless air track is tied to a spring. Positions are measured from the left end of the track, with right as positive, and the glider's equilibrium position is $x = 0.50$ m. When the glider is at $x = 0.53$ m, the net force on it is $- 1.2$ N. What is the net force on it when it is at $x = 0.425$ m?

Your answer N

Question 7 · from 7.2 · Decide and justify

A pendulum clock ticks once per swing and keeps perfect time in a cool room. Its pendulum is a small, heavy bob on a light brass rod, so treat it as a simple pendulum swinging through a small angle. On a hot day the rod lengthens slightly. On the hot day, does the clock run slow or fast?

Which reason supports your answer?

Question 8 · from 7.3 · Multiple choice

A 0.50 kg cart on a level track is attached to one end of a spring with spring constant 200 N/m. A motor moves the spring's other end back and forth sinusoidally, at a frequency a student can set. At which driving frequency does the cart's amplitude grow largest?

Setup for question 9

On paper. Describe how you would test, in your lab, whether a cart on a spring on a level track keeps the same total energy as it oscillates. Say what you would measure and with what equipment, what you would calculate from each set of readings, and what graph you would make to judge the result. There is nothing to submit here; compare your plan with the readings in Check yourself.

Question 9 · from 7.4 · Sketch the graph

A 1.0 kg block on a level, frictionless surface is attached to a spring with spring constant 500 N/m and oscillates with amplitude 0.10 m about equilibrium at $x = 0$ ; right is positive. Sketch the system's kinetic energy against the block's position from $x = 0$ to $x = + 0.10$ m.

Drag a point up or down, or tap it and use the arrow keys. Only the shape is checked.

Setup for question 10

A science museum hangs a horizontal disk from a thin vertical steel wire attached at the disk's center, so the disk can twist back and forth about the wire. Take counterclockwise as seen from above as positive, with $θ = 0$ where the wire is untwisted. Twisted through $Δ θ$ , the wire exerts a torque $- k Δ θ$ on the disk. Staff hang three different disks on the same wire, twist each to 0.40 rad, release it and time the oscillation:

Disks on the museum's wire
Disk	$I$ about the wire (kg·m²)	Period (s)
P	0.050	0.99
Q	0.100	1.40
R	0.200	1.99

Question 10 · from 7.5 · Calculate

Using disk R's row of the table, what is the wire's torsion constant $k$ ?

Your answer N·m/rad

0 of 10 answered.