12.1.
Solve: (b)
Model: Model the sun (s), the earth (e), and the moon (m) as spherical. (a)
Fs on e =
Gms me (6.67 10 -11 N m 2 / kg 2 )(1.99 10 30 kg)(5.98 10 24 kg) = 3.53 10 22 N = (1.50 1011 m ) 2 rs2 e -
Fm on e =
GMm Me (6.67 10 -1
13.1. Model: The crankshaft is a rotating rigid body.
Solve: The crankshaft at t = 0 s has an angular velocity of 250 rad/s. It gradually slows down to 50 rad/s in 2 s, maintains a constant angular velocity for 2 s until t = 4 s, and then speeds up
14.1. Solve: The frequency generated by a guitar string is 440 Hz. The period is the inverse of the frequency, hence
T= 1 1 = = 2.27 10 -3 s = 2.27 ms f 440 Hz
14.2. Solve: Your pulse or heart beat is 75 beats per minute. The frequency of your hear
15.1. Solve: The density of the liquid is
=
m 0.120 kg 0.120 kg = = = 1200 kg m 3 V 100 mL 100 10 -3 10 -3 m 3
Assess: The liquid's density is more than that of water (1000 kg/m3) and is a reasonable number.
15.2. Solve: The volume of the helium
2.1.
Solve:
Model: The car is represented by the particle model as a dot. (a) Time t (s) Position x (m) 0 1200 1 975 2 825 3 750 4 700 5 650 6 600 7 500 8 300 9 0
(b)
2.2. Solve:
Diagram (a) (b) (c)
Position Negative Negative Positive
Velocity
3.1. Solve: (a) If one component of the vector is zero, then the other component must not be zero (unless the whole vector is zero). Thus the magnitude of the vector will be the value of the other component. For example, if Ax = 0 m and Ay = 5 m, the
4.1. Solve: A force is basically a push or a pull on an object. There are five basic characteristics of forces. (i) A force has an agent that is the direct and immediate source of the push or pull. (ii) Most forces are contact forces that occur at a
8.1. Visualize:
Solve: Figure (i) shows a weightlifter (WL) holding a heavy barbell (BB) across his shoulders. He is standing on a rough surface (S) that is a part of the earth (E). We distinguish between the surface (S), which exerts a contact forc
Physics 133 11:30 Winter 2008 QUIZ 3 January 31, 2008
Name /\ V
Instructor: Barrett Davis George Hinton Knobbe
Note: Circle the name of your instructor (above).
Note: There are 15 minutes for this quiz.
Note: There is one problem with four parts
Please pick up your clicker
Ideal and damped oscillations
In ideal oscillations, the total energy is conserved:
1 mv 2 2
1 2 kx 2
mgh
time 1
1 mv 2 2
1 2 kx 2
mgh
time 2
In damped oscillations, energy is lost with time:
X '
Xme
2
bt 2m
Please pick up the clicker with your assigned number. Remember the number, as you will use the same clicker for the entire quarter.
Review of Lecture 2 on March 26, 2008
A linear restoring force is required for simple harmonic motion:
X X m cost
Please pick up your clicker
Review of traveling waves
Old formulas:
y y m sinkx t wave traveling to the right. y y m sinkx t wave traveling to the left. 2 k + to left, and to right 2f v f k History graph of amplitude versus time a
Please pick up your clicker
Review of traveling waves
y y m sinkx t wave traveling to the right. y y m sinkx t wave traveling to the left. 2 k + to left, and to right 2f v f k History graph of amplitude versus time at a sin gle x p
5.1.
Model: We can assume that the ring is a single massless particle in static equilibrium. Visualize:
Solve:
Written in component form, Newton's first law is
( Fnet ) x = Fx = T1x + T2 x + T3 x = 0 N
T1 x = - T1
T1y = 0 N Using Newton's first l
16.1. Solve: The mass of lead mPb = Pb VPb = (11,300 kg m 3 )(2.0 m 3 ) = 22,600 kg . For water to have the
same mass its volume must be
Vwater =
mwater 22,600 kg = = 22.6 m 3 water 1000 kg m 3
16.2. Solve: The volume of the uranium nucleus is
V
17.1. Model: For a gas, the thermal energy is the total kinetic energy of the moving molecules. That is, Eth =
Kmicro. Solve: The number of atoms is
N=
M 0.0020 kg = = 3.01 10 23 m 6.64 10 -27 kg
Because helium atoms have an atomic mass number A
6.1. Model: We will assume motion under constant-acceleration kinematics in a plane.
Visualize:
Instead of working with the components of position, velocity, and acceleration in the x and y directions, we will use the kinematic equations in vector f
7.1. Solve: (a) From t = 0 s to t = 1 s the particle rotates clockwise from the angular position +4 rad to -2 rad. Therefore, = -2 - ( +4 ) = -6 rad in one sec, or = -6 rad s . From t = 1 s to t = 2 s, = 0 rad/s. From t = 2 s to t = 4 s the partic
18.1. Solve: We can use the ideal-gas law in the form pV = NkBT to determine the Loschmidt number (N/V):
1.013 10 5 Pa N p = 2.69 10 25 m -3 = = V kB T (1.38 10 -23 J K )(273 K )
(
)
18.2. Solve: Nitrogen is a diatomic molecule, so r 1.0 10-1
19.1. Model: The heat engine follows a closed cycle, starting and ending in the original state. The cycle
consists of three individual processes. Visualize: Please refer to Figure Ex19.1. Solve: (a) The work done by the heat engine per cycle is the a