Name:

Physics 161

Final Exam Summer I '01

7/13/2001

Jeff Simpson

There are 6 questions worth 20 points each with point breakdowns listed in square brackets. Show ALL your work. If you need more workspace, use the back of the same page and write a note indicating this.

1. A few questions
(a) [6 pts] Describe what is meant by an inertial and a non-inertial reference frame. Compare the two in terms of how an observer in each might apply Newton's laws.

(b) [6 pts] How are linear and angular momentum related? When is linear momentum conserved? When is angular momentum conserved?

(c) [8 pts] An astronaut on a research mission to asteroid 1566, named Icarus, ponders whether she can escape the asteroid's gravitational pull simply by jumping upwards from the surface. Icarus has a diameter of $1.4\,$km and a mass of $10^{12}\,$kg and the universal gravitational constant $G=6.67 \times 10^{-11}\,$N$\cdot$m$^2$/kg$^2$. Calculate the escape speed of Icarus and comment whether a person might achieve this speed by jumping.

2. A puck of mass $m_1=0.30\,$kg initially at rest on a horizontal, frictionless surface, is struck by a second puck of mass $m_2=0.20\,$kg. The second puck is moving initially with speed $v_i=2.00\,$m/s in the positive $x$ direction and after the collision moves with a speed $v_{2f}=1.00\,$m/s at an angle $\theta=53.0^\circ$ from the positive $x$ axis.

(a) [8 pts] Determine the velocity of the first puck $m_1$ after the collision.

(b) [7 pts] Find the fraction of kinetic energy lost in the collision ($\Delta K/K_i$). Where does this energy go?

(c) [5 pts] What is the impulse delivered to puck $m_1$?

3. The velocity versus time graph for an object traveling along a straight line is given below. The initial position of the object at $t=0\,$s is $0\,$m.
(a) [7 pts] Graph the acceleration versus time on the bottom graph. Include numeric values on the acceleration axis (ordinate axis) to indicate the scale.
(b) [7 pts] Graph the position versus time on the top graph. Include numeric values on the position axis (ordinate axis) to indicate the scale.
(c) [6 pts] What is the value of the position at $t=5, 15,$ and 25 seconds?

4. Several constant forces are applied to a wheel as shown. Note $F_1$ is applied at an angle $\theta=20^\circ$ relative to the tangent. The values of the radii are given by $r_1=30\,$cm and $r_2=45\,$cm. The wheel has a mass $M=2\,$kg and can be considered to be a uniform disk of radius $r_2$.

(a) [5 pts] Find the net torque acting on the wheel. Reminder: torque is a vector.

(b) [5 pts] If the torque in part (a) acts continuously on the wheel, which is initially at rest, find the angular speed after 3.0 seconds.

(c) [5 pts] How many revolutions does the wheel make during this time?

(d) [5 pts] What is the net work done on the wheel?

5. A wad of putty with mass $m$ travels with initial speed $v_i$. The putty hits and sticks to the end of a uniform rod of length $l$ and mass $M$. The rod is free to rotate in a horizontal plane about a fixed vertical axis through its center of mass. Where appropriate, express your answers in terms of $m, M, v_i,$ and $l$.

(a) [3 pts] Find the initial angular momentum $\bm{L}_i$ of the putty about the axis of the rod. Be sure to specify magnitude and direction.

(b) [5 pts] Calculate the moment of inertia of the putty and rod about the axis of the rod.

(c) [6 pts] What is the final angular velocity $\bm{\omega}_f$ of the putty and rod? Remember that angular velocity is a vector.

(d) [6 pts] Suppose that after hitting the rod the putty did not stick but instead continued traveling in the same direction with speed $v_f=\frac{1}{2}\,v_i$. Find the angular velocity of the rod in this case.

6. A cart of mass $m$ is released from a height $h$ such that it just makes the loop of radius $R$ as shown. After the loop the cart slides off of the end of the track which is a distance $H$ above the ground. The track is frictionless. Where appropriate, express your answers in terms of $R, H,$ and $g$.

(a) [6 pts] Find the initial height $h$.

(b) [4 pts] What is the speed of the cart after completing the loop?

(c) [4 pts] Find the distance $d$ where the cart lands.

(d) [6 pts] Label a two-component coordinate system for the cart's motion after the end of the track. For each component sketch the position, velocity, and acceleration versus time.