Question 1

A satellite of mass $$m$$ moves in an elliptical orbit around the Earth. At point $$C$$, the satellite is at a distance $$r_C$$ from the center of the Earth and has speed $$v_C. $$Which of the following correctly expresses the total mechanical energy $$E of $$the satellite at point $$C$$?

Accepted Answer

$$E = \dfrac{1}{2} m v_C^2$ - \dfrac{G M_E m}{r_C}$$

Question 2

A standing wave is formed in a tube of length $$L. $$The pressure variation graph shows a node at $$x = 0$$ and an antinode at $$x = L. $$What type of tube is this?

Accepted Answer

Open at one end and closed at the other

Question 3

A torsion balance is used to measure the gravitational constant $$G. If $$the torsion constant of the wire is $$K$$ and the period of oscillation is $$T$$, what is the correct formula for $$K$$?

Accepted Answer

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

Question 4

A non-viscous, incompressible fluid flows through a horizontal tube with varying diameter. At point 1, the cross-sectional area is $$A_1$$ and the velocity is $$v_1. At $$point 2, the area is $$A_2. $$What is the velocity $$v_2 at $$point 2?

Accepted Answer

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

Question 5

A block of mass $$m$$ attached to a spring of stiffness $$k$$ oscillates with angular frequency $$\omega. $$What is the correct expression for $$\omega$$?

Accepted Answer

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

Question 6

A solid disk of mass $$M$$ and radius $$R$$ rolls down a track without slipping. What is the correct expression for its moment of inertia $$I$$ about its center?

Accepted Answer

$$I = \dfrac{1}{2} M R^2$

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 differential equation governing the velocity $$v of $$the cannon as a function of time?

Accepted Answer

$$(m - \alpha t) \dfrac{dv}{dt} = \alpha v_0$

Question 8

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

Accepted Answer

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

Question 9

A block of mass $$m$$ attached to a spring oscillates with amplitude $$A. $$What is the total mechanical energy $$E of $$the oscillator?

Accepted Answer

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

Question 10

A fluid flows through a horizontal pipe. At point 1, the pressure is $$P_1$$ and the velocity is $$v_1. At $$point 2, the pressure is $$P_2$$ and the velocity is $$v_2. $$Which equation correctly relates $$P_1$$, $$v_1$$, $$P_2$$, and $$v_2$$ according to Bernoulli's principle?

Accepted Answer

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

Question 11

A projectile is launched horizontally from a height $$h$$ above the ground with initial speed $$v_0. $$What is the time $$t it $$takes to hit the ground?

Accepted Answer

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

Question 12

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping. What is its rotational kinetic energy when moving at speed $$v$$?

Accepted Answer

$$K_{rot} = \dfrac{1}{2} I \$$omega^2$$ = \dfrac{1}{5} M v^2$

Question 13

A tube of length $$L is $$open at both ends. What is the fundamental frequency $$f_1 of $$the standing wave in the tube if the speed of sound is $$v$$?

Accepted Answer

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

Question 14

A block of mass $$m is $$attached to a spring and oscillates with position $$x(t) = A \cos(\omega t + \phi). $$What is the velocity $$v(t) of $$the block as a function of time?

Accepted Answer

$$v(t) = -A \omega \sin(\omega t + \phi)$$

Question 15

A disk of mass $$M$$ and radius $$R$$ rolls off a track and becomes a projectile. What is the maximum height $$H it $$reaches above the end of the track if its speed at the end is $$v$$?

Accepted Answer

$$H = \dfrac{v^2$}{2g}$$

Question 16

A torsion balance is used to measure $$G by $$observing the equilibrium of forces between two masses. Which force law is used to describe the gravitational attraction between the masses?

Accepted Answer

$$F = G \dfrac{m_1$ m_2$}{r^2$}$$

Question 17

A block of mass $$m is $$dropped from height $$h$$ and sticks to a spring of constant $$k. $$What is the maximum compression $$x_{max} of $$the spring?

Accepted Answer

$$x_{max} = \sqrt{\dfrac{2 m g h}{k}}$$

Question 18

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the horizontal distance $$R it $$travels before hitting the ground?

Accepted Answer

$$R = \dfrac{v_0$^2 \sin(2	heta)}{g}$$

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

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