IQS Physics S2 Test

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Physics Questions (5 pts. apiece) Answer in complete, well-written sentences ONLY WITHIN the spaces provided.

1. Recall the laboratory Periodic Motion where you measured the motion of a harmonic oscillator. When the mass has its maximum velocity, is its distance from the motion sensor maximum, minimum, the equilibrium value, or some other value?

   
   
   
   
   
   
   
   

2. You are on a white horse, riding off at sunset with your beau on a chestnut mare riding at your side. Your horse has a speed of $2.7~ m/s$ and your beau's horse has a speed of $3.0~ m/s$, yet he/she constantly remains at your side. Where are your horses? Describe the motion. Make a sketch to explain your answer.

   
   
   

   
   
   

3. Recall the laboratory entitled Newton's Second Law for Rotation where you applied a torque to a rotator using a pulley and a weight on a string. What is the formula for the torque on the rotating system as a function of the magnitude of the hanging mass $m$ and radius, , of the spool? Describe each variable in your equation.

   
   
   
   
   
   
   
   

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4. A bola consists of three heavy balls connected to a common point by three equal lengths of sturdy string. It is readied for launch by holding one of the balls overhead and rotating the wrist, causing the other two balls to rotate in a horizontal circle about the hand. See figure (a) below. The bola is then released and its configuration rapidly changes from that shown in the overhead view of the left-hand side of the figure below (a) to the one on the right-hand side (b). During this change in configuration does the angular speed of the bola about its center of mass increase, decrease, or stay the same? Explain.

   
   
   

   
   
   
   

DO NOT WRITE BELOW THIS LINE.

Problems (3). Clearly show all reasoning for full credit. Show all work on the page below each problem.

1.

7 pts.

A block of unknown mass is attached to a spring with a force constant $k=7~N/m$ and undergoes simple harmonic motion with an amplitude $A=0.08~m$. When the block is halfway between its equilibrium position and the end point, its speed is measured to be $v_1 = 0.2~m/s$. What is the mass of the block and the period of the motion?

See next page.

2.

8 pts.

The tub of a washer goes into its spin cycle, starting from rest and gaining angular speed uniformly for $10~s$ at which time it is turning at a rate of $5~rev/s$. At this point the person doing the laundry opens the lid and a safety switch turns off the washer. The tub smoothly slows to rest in $6~s$. Through how many revolutions does the tub turn while it is in motion?

See next page.

3.

10 pts.

A hoop of mass $M$ and radius $R$ rotates about an axle at the edge of the hoop. The hoop starts at its highest position and is given a very small push to start it rotating. At its lowest position, what is the angular velocity of the hoop? What is the speed of the lowest point on the hoop?

Physics Constants, Conversion Factors, and Equations

$$x(t) = \frac{1}{2}at^2 + v_0t + y_0 \quad v = at + v_0 \quad... ...d \omega = \alpha t + \omega_0 \quad a_c = \frac{v^2}{r} \quad$$

$$\theta = {s \over r} \quad \omega = {v_T \over r} = {d\theta... ...ega \over dt} \quad I = \sum m_i r_i^2 = I_{cm} + MR^2 \quad$$

$$x(t) = A\cos (\omega t + \phi) \quad \mu = \frac{m_1m_2}{m_1... ... \frac{k}{m} \quad T = \frac{2\pi}{\omega} = \frac{1}{f} \quad$$

$$\Delta E = h\nu \quad E=(n+\frac{1}{2})\hbar\omega \quad \hbar = \frac{h}{2\pi}$$

$$\vec F_{net} = \sum_i \vec F_i = m \vec a = \frac{d\vec p}{d... ...quad \overline {\vec F} = \frac{\Delta \vec p}{\Delta t} \quad$$

$$\vert\vec F_f\vert = \mu N \quad \vert\vec F_c\vert = m \fra... ...} \quad \vec F_s(x) = -kx\hat i \quad \vec F_g(y) = -mg\hat j$$

$$W = \int \vec F \cdot d\vec s = \int \vert\vec F\vert \ver... ...PE \quad KE = \frac{1}{2} mv^2 \quad KE = \frac{1}{2}I\omega^2$$

$$PE_g = mgh \quad PE_s = \frac{1}{2}kx^2 \quad ME_0 = ME_1 \quad \vec p = m \vec v \quad \vec p_0 = \vec p_1 \quad$$

$$\vert\vec \tau \vert = r F\sin\phi = I\alpha = \left \vert\f... ... \omega = rmv\sin \phi \quad L_0 = L_1 \quad v_{cm} = r\omega$$

$$\vec A = A_x \hat i + A_y \hat j + A_z \hat k \quad {dA \ove... ...os\theta \quad \frac{d\cos\theta}{d\theta} = -\sin\theta \quad$$

$$\langle x\rangle = \frac{1}{N}\sum_i x_{i} \quad \sigma = \s... ...} \quad A = 4\pi r^2 \quad V = Ah \quad V = {4\over 3} \pi r^3$$

$$\frac{d f(x)}{dx} = \lim_{\Delta x \rightarrow 0} \frac{f(x+... ...f(x) \Delta x \quad \frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}$$

Speed of Light ($c$)	$2.9979\times 10^8~m/s$	proton/neutron mass	$1.67\times 10^{-27}~kg$
$R$	$8.31J/K-mole$	$g$	$9.8~m/s^2$
Earth's mass	$5.98 \times 10^{24}~kg$	Earth's radius	$6.37\times 10^6~m$
Earth-Moon distance	$3.84\times 10^8~m$	Electron mass	$9.11\times 10^{-31}~kg$
$h$	$6.626\times 10^{-34}~J-s$	$1.6\times 10^{-19}~J/eV$	$1.66\times 10^{-27}~kg/u$