Question 1

Two simple pendulums are identical except the first is half the length of the second. If the natural frequency of the first is $$f$$, what is the natural frequency of the second?

Accepted Answer

$$f/\sqrt{2}$$

Question 2

A box of mass $$m is $$pressed against an ideal spring (force constant $$k$$), compressing it a distance $$x. $$After release, the box slides up a frictionless incline and stops. If the experiment is repeated with a box of mass $$2m$$, what happens to the maximum height reached?

Accepted Answer

Both boxes reach the same maximum height.

Question 3

An open railroad car filled with coal is coasting frictionlessly in the $$+x$$ direction. A girl in the car throws coal backward in the $$-x$$ direction. What happens to the speed of the car?

Accepted Answer

The car speeds up.

Question 4

If $$\vec{A}$$ and $$\vec{B}$$ are nonzero vectors and $$\vec{A} \cdot \vec{B} = 0$$, what must be true?

Accepted Answer

$$\vec{A} is $$perpendicular to $$\vec{B}$$

Question 5

A uniform rod of mass $$M$$ and length $$L$$ rotates about its center. Two beads of mass $$m$$ are initially at distance $$	heta$$ from the axis. If the beads slide to the ends of the rod, what is the final angular velocity $$\omega_f in $$terms of $$\omega_i$$, $$M$$, $$L$$, $$m$$, and $$	heta$$?

Accepted Answer

$$\omega_f = \omega_i \frac{\frac{1}{12}ML^2$ + 2m\$$theta^2$$}{\frac{1}{12}ML^2$ + 2m\left(\frac{L}{2}\$$right)^2$$}$$

Question 6

A solid ball of radius $$R$$ rolls without slipping down a ramp from rest. At the end, it leaves from height $$h at $$angle $$\phi to $$the horizontal and lands after time $$t. $$What is the initial height $$H$$ from which it was released?

Accepted Answer

$$H = h + \frac{1}{2}g t^2$

Question 7

A ladder rests between a glass wall and a grassy lawn. The coefficient of static friction between the ladder and the grass is $$\mu_s$$, and there is no friction at the wall. What is the smallest angle $$	heta$$ the ladder can make with the ground without slipping?

Accepted Answer

$$	an 	heta = 2 \mu_s$$

Question 8

A baseball is thrown horizontally from the surface of Phobos (radius $$R$$, mass $$M) so $$that it orbits. What speed $$v$$ must it be thrown at?

Accepted Answer

$$v = \sqrt{\frac{GM}{R}}$$

Question 9

An object has initial momentum $$\vec{p}_i = b \hat{i}. A $$force $$\vec{F}(t) = c t \hat{i} + d t^2$ \hat{j} is $$applied from $$t=0 to$$ $$t=t_f. $$What is the magnitude of the object's momentum at $$t = t_f$$?

Accepted Answer

$$\sqrt{\left(b + \frac{1}{2} c t_f^2$ \$$right)^2$$ + \left(\frac{1}{3} d t_f^3$ \$$right)^2$$}$$

Question 10

Two professors push against a wall for different times. Prof. Robertson pushes for 10 min, Prof. Smith for 15 min. Compare the work they do.

Accepted Answer

Neither of them does any work.

Question 11

Two wooden blocks with different masses are stacked on a table. In which case is the force that the bottom block exerts on the top block the greatest?

Accepted Answer

Stack C: 300 g on bottom, 100 g on top.

Question 12

Which of the following best describes the relationship between impulse and momentum?

Accepted Answer

Impulse equals the change in momentum: $$\vec{J} = \Delta \vec{p}$$

Question 13

A solid sphere of mass $$m$$ and radius $$R$$ rolls without slipping down a ramp. What is the total kinetic energy at the bottom?

Accepted Answer

$$K = \frac{7}{10} m v^2$

Question 14

A block slides up a frictionless incline after being released from a compressed spring. Which principle allows you to determine the maximum height reached?

Accepted Answer

Conservation of energy

Question 15

A ball is thrown horizontally from a height $$h$$ and lands after time $$t. $$What is the vertical component of its velocity just before it hits the ground?

Accepted Answer

$$v_y = g t$$

Question 16

Which equation correctly relates the moment of inertia $$I of a $$uniform rod of mass $$M$$ and length $$L$$ about its center?

Accepted Answer

$$I = \frac{1}{12} M L^2$

Question 17

A block is pressed against a spring and released. If the spring is compressed by $$x$$, what is the speed $$v of $$the block as it leaves the spring (mass $$m$$, spring constant $$k$$)?

Accepted Answer

$$v = \sqrt{\frac{k}{m}} x$$

Question 18

Which of the following is true for a simple harmonic oscillator with amplitude $$A$$ and angular frequency $$\omega$$?

Accepted Answer

The maximum speed is $$v_{max} = A \omega$$

Question 19

A solid ball rolls down a ramp and leaves at angle $$\phi to $$the horizontal. Which kinematic equation relates the horizontal distance $$d it $$travels to its initial velocity $$v_0$$ and time $$t$$?

Accepted Answer

$$d = v_0$ \cos \phi \cdot t$$

Physics 10310 Final Exam Study Guidance

Study Guide - Practice Questions

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