Q: A block of mass $$m$$ slides down a frictionless incline of height $$h$$ and then moves horizontally off a table. What is the horizontal distance $$d it $$travels before hitting the ground?

$$d = v_0$ t$$,\ \text{where}\ $$v_0$$ = \sqrt{2gh}$$ and t$$ = \sqrt{\dfrac{2H}{g}}$

Question 1

A satellite of mass $$m$$ moves in an elliptical orbit around the Earth. At point $$A ($$closest approach), its distance from the center of the Earth is $$r_A$$ and its speed is $$v_A. At $$point $$C ($$farthest distance), its distance is $$r_C. $$Neglecting air resistance, what is the speed $$v_C of $$the satellite at point $$C$$?

Accepted Answer

$$v_C = v_A \dfrac{r_A}{r_C} ($$from conservation of angular momentum)

Question 2

A standing wave is formed in a tube of length $$L. $$The pressure node pattern shows nodes at both ends. Which of the following statements is correct?

Accepted Answer

The tube is open at both ends.

Question 3

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

Accepted Answer

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

Question 4

A non-viscous, incompressible fluid flows through a horizontal tube with varying cross-sectional area. At point 1, the 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 $$m is $$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

$$v = \sqrt{\dfrac{2gh}{1 + \dfrac{1}{2}}}$$

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 for the velocity $$v of $$the cannon as a function of time?

Accepted Answer

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

Question 8

A block of mass $$m is $$released from rest at $$x = A on a $$spring-mass system. What is the equation for its position as a function of time?

Accepted Answer

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

Question 9

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

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

Question 10

A tube of length $$L is $$open at one end and closed at the other. 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}{4L}$$

Question 11

A block of mass $$m$$ slides down a frictionless incline of height $$h$$ and then moves horizontally off a table. What is the horizontal distance $$d it $$travels before hitting the ground?

Accepted Answer

$$d = v_0$ t$$,\ 	ext{where}\ $$v_0$$ = \sqrt{2gh}$$ and t$$ = \sqrt{\dfrac{2H}{g}}$

Question 12

A manometer is used to measure the pressure difference between two points in a fluid. If the height difference in the manometer is $$h$$ and the density of the manometer fluid is $$\rho$$, what is the pressure difference $$\Delta P$$?

Accepted Answer

$$\Delta P = \rho g h$$

Question 13

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping. What is its moment of inertia about its center?

Accepted Answer

$$I = \dfrac{2}{5} M R^2$

Question 14

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

Accepted Answer

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

Question 15

A disk of mass $$M$$ and radius $$R is $$rolling without slipping at speed $$v. $$What is its total kinetic energy?

Accepted Answer

$$K = \dfrac{1}{2} M v^2$ + \dfrac{1}{2} I \$$omega^2$$

Question 16

A fluid flows through a pipe that narrows from area $$A_1 to$$ $$A_2. If $$the pressure at the wide section is $$P_1$$ and at the narrow section is $$P_2$$, which equation relates the pressures and velocities at the two points?

Accepted Answer

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

Question 17

A block of mass $$m is $$dropped from a height $$h. $$What is its speed just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 18

A solid cylinder of mass $$M$$ and radius $$R$$ rotates about its central axis. What is its moment of inertia?

Accepted Answer

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

Question 19

A block of mass $$m is $$moving with velocity $$v$$ and collides elastically with a stationary block of mass $$M. $$What is the final velocity of the block of mass $$m$$ after the collision?

Accepted Answer

$$v' = \dfrac{m - M}{m + M} v$$

Physics 7A: Core Concepts and Problem-Solving Guide

Study Guide - Practice Questions

Study Guide - Flashcards