Question 1

A satellite of mass $$m is in an $$elliptical orbit around the Earth. At point A, it is at a distance $$r_A$$ from the center of the Earth and has speed $$v_A. At $$point C, it is at a distance $$r_C$$ from the center of the Earth. Neglecting air resistance, what is the speed $$v_C of $$the satellite at point C?

Accepted Answer

$$v_C = v_A \dfrac{r_C}{r_A}$$

Question 2

A standing wave is formed in a tube of length $$L. $$The pressure node pattern shows two nodes at both ends and one antinode in the middle. What is the fundamental frequency $$f_1 of $$the tube if the speed of sound is $$v$$?

Accepted Answer

$$f_1$$ = \dfrac{v}{2L}$$

Question 3

A torsion balance is used to measure the gravitational constant $$G. $$Two small masses $$m$$ are attached to the ends of a rod of length $$L$$ and suspended by a thin wire. Two large masses $$M$$ are placed near the small masses. If the period of oscillation of the balance is $$T$$, what is the torsional constant $$\kappa of $$the wire?

Accepted Answer

$$\kappa = \dfrac{4\pi^2$ I}{T^2$}$$

Question 4

A non-viscous, incompressible fluid flows through a horizontal tube that narrows from area $$A_1 to$$ $$A_2. If $$the velocity at point 1 is $$v_1$$, what is the velocity at point 2, $$v_2$$?

Accepted Answer

$$v_2$$ = $$v_1$$ \dfrac{$$A_1$$}{$$A_2$$}$$

Question 5

A block of mass $$m is $$attached to an ideal spring of stiffness $$k$$ and oscillates on a frictionless surface. What is the angular frequency $$\omega of $$the oscillator?

Accepted Answer

$$\omega = \sqrt{\dfrac{k}{m}}$$

Question 6

A solid disk of mass $$M$$ and radius $$R$$ rolls without slipping down a track of height $$h. $$What is the speed $$v of $$the disk at the bottom of the track?

Accepted Answer

$$v = \sqrt{\dfrac{4gh}{3}}$$

Question 7

A water cannon of mass $$M$$ ejects water at a constant rate $$\alpha$$ with velocity $$v_0$$ relative to the cannon. What is the velocity $$v(t) of $$the cannon as a function of time, assuming it starts from rest and the mass of water ejected is much less than $$M$$?

Accepted Answer

$$v(t) = \dfrac{\alpha v_0$}{M} t$$

Question 8

A block of mass $$m is $$released from rest at $$x_0 on a $$spring with force constant $$k. $$What is the equation for the position $$x(t) as a $$function of time?

Accepted Answer

$$x(t) = x_0$ \cos(\omega t)$$

Question 9

A disk leaves a track horizontally with speed $$v_0$$ and lands at a horizontal distance $$d$$ from the end of the track. Neglecting air resistance, what is the time $$t it $$takes to hit the ground from height $$h$$?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 10

A tube of length $$L is $$open at one end and closed at the other. What is the wavelength $$\$$lambda_1$$ of the fundamental mode?

Accepted Answer

$$\$$lambda_1$$ = 4L$$

Question 11

A fluid flows through a horizontal pipe with a manometer attached as shown. If the height difference in the manometer is $$h$$, what is the pressure difference $$P_1$$ - $$P_2$$ between the two points?

Accepted Answer

$$P_1$$ - $$P_2$$ = \rho g h$$

Question 12

A block of mass $$m$$ moving with velocity $$v$$ collides and sticks to another block of mass $$M at $$rest. What is the final velocity $$v_f of $$the combined mass?

Accepted Answer

$$v_f = \dfrac{mv}{m+M}$$

Question 13

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping down a ramp of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{\dfrac{10gh}{7}}$$

Question 14

A torsion balance is used to measure $$G. If $$the gravitational force between two masses $$m$$ and $$M$$ separated by distance $$r is$$ $$F$$, what is the value of $$G$$?

Accepted Answer

$$G = \dfrac{F r^2$}{m M}$$

Question 15

A block attached to a spring oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is the total mechanical energy $$E of $$the oscillator?

Accepted Answer

$$E = \dfrac{1}{2} k A^2$

Question 16

A projectile is launched horizontally from a height $$h$$ with speed $$v_0. $$What is the maximum height $$H$$ above the ground it reaches?

Accepted Answer

$$H = h$$

Question 17

A thin rod of length $$L$$ and mass $$M$$ rotates about one end. What is its moment of inertia?

Accepted Answer

$$I = \dfrac{1}{3} M L^2$

Question 18

A block of mass $$m is $$attached to a spring and oscillates with period $$T. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \dfrac{4\pi^2$ m}{T^2$}$$

Question 19

A fluid flows through a pipe with a constriction. If the pressure at the wide section is $$P_1$$ and at the narrow section is $$P_2$$, and the fluid speeds are $$v_1$$ and $$v_2$$ respectively, which equation expresses Bernoulli's principle?

Accepted Answer

$$P_1$$ + \dfrac{1}{2} \rho $$v_1^2$$ = $$P_2$$ + \dfrac{1}{2} \rho $$v_2^2$

Physics 7A Final Exam Study Guide: Classical Mechanics, Fluids, and Oscillations

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