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

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

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 $$T$$, which equation correctly relates $$K$$ and $$T$$?

Accepted Answer

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

Question 4

A non-viscous, incompressible fluid flows through a horizontal tube with varying diameter. At point 1, the tube is narrow, and at point 2, the tube is wide. Which statement about the fluid velocity at points 1 and 2 is correct?

Accepted Answer

The velocity at point 1 is greater than at point 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

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

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 about its center?

Accepted Answer

$$I = \frac{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 motion of the cannon?

Accepted Answer

$$m \frac{dv}{dt} = -\alpha v_0$

Question 8

A block of mass $$m is $$released from rest at position $$x_0 on a $$frictionless surface attached to a spring. What is the equation for its position as a function of time?

Accepted Answer

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

Question 9

A disk of mass $$M$$ and radius $$R$$ rolls off a track and becomes a projectile. Neglecting air resistance, what is the maximum height $$H$$ reached above the end of the track if its speed at launch is $$v_0$$?

Accepted Answer

$$H = \frac{v_0$^2}{2g}$$

Question 10

A fluid flows through a horizontal tube and is measured by a manometer. If the height difference in the manometer is $$h$$ and the density of the manometer fluid is $$\rho_m$$, what is the pressure difference $$\Delta P$$ between the two points?

Accepted Answer

$$\Delta P = \rho_m g h$$

Question 11

A block of mass $$m$$ oscillates on a spring with amplitude $$A$$ and angular frequency $$\omega. $$What is the total mechanical energy of the oscillator?

Accepted Answer

$$E = \frac{1}{2} m \$$omega^2$$ A^2$

Question 12

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

Accepted Answer

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

Question 13

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping down an incline. What fraction of its total kinetic energy is rotational at the bottom?

Accepted Answer

$$\frac{2}{7}$$

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

A disk of mass $$M$$ and radius $$R$$ rolls off a table with speed $$v_0. $$What is its angular speed $$\omega$$ just before hitting the ground?

Accepted Answer

$$\omega = \frac{v_0$}{R}$$

Question 17

A water cannon ejects water at a constant rate $$\alpha$$ and velocity $$v_0. $$What happens to the velocity of the cannon once it is empty?

Accepted Answer

It remains constant at its final value

Question 18

A torsion balance is used to measure $$G. If $$the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by distance $$r is$$ $$F$$, which equation gives $$G$$?

Accepted Answer

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

Question 19

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

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

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

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