Phys223Exam 2 RedoName: ______
Score: ______
Only redo the problems for which you did not receive a full score. The instructions have changed. Read them!
Your workmustbe concise, legible and clear. I must understand your reasoning immediately. Think first, then write.
Problem 1. The intensity at a distance of 6.0 m from a source that is radiating equally in all directions is 6.0 × 10-10 W/m2. What is the power emitted by the source?
Show that the power emitted by the source is 2.7 × 10-7 W.
Problem 2
Phys223Exam 2 RedoName: ______
Score: ______
The figure shows a history graph at x=0m of a wave traveling on a string in the negative x-direction with a speed of 4 m/s.
Phys223Exam 2 RedoName: ______
Score: ______
a. Find and explain how you find the following quantities. Don’t forget units.
T=
A=
The displacement equation for a wave traveling in the positive x-direction is . Write the displacement equation for a wave traveling in the negative x-direction.
Write your displacement equation with numbers only (no units).
b. What is the wave velocity in this case?
c. Write the equation for theparticle velocityas a function of x and t, i.e. v(x,t).
d. Write the equation for the particle velocity at x=3m. What does this equation give you?
e. Use your answer from part (a) to find the displacement at t=1/2T. Note: this is giving the displacement at one moment in time and at all locations, i.e. this is a snapshot graph.
f. Sketch thesnapshot graph of the wave at t=1/2 T, where T is the period.
g. If the string is replaced by one made of the same material and under the same tension but having twice the radius, what will be the wave speed? Hint: depends on mass and length. How does the mass change if the string is thicker (same material)?
Problem 3 Explain your work
The SHM oscillation of a horizontal mass-spring system (no friction, mass m=4kg) is shown below.
a. Find and explain how you find the following quantities. Don’t forget units.
T=
A=
Write your displacement equation with numbers only (no units). x(t)=Acos(t+0)
b. Find the equation for the mass’s velocity as a function of time. Also find the equation for the mass’s acceleration as a function of time.
v(t)=
a(t)=
Sketch the v-t behavior of the mass on the axes above. Don’t forget the scale (i.e. max velocity).
Check: The graph should match your equation in b and it should be the slope of the x-t graph given above. Make sure everything is consistent.
c. The total energy in the mass-spring system is given by , where v is the speed when the mass is at location x and k is the spring constant. Note that k is NOT the wave number, there is no wave number because we are not dealing with a traveling wave!!!
You can find the total energy by using the above equation for any point x (and corresponding speed v). However, it is often easier to look at points where all energy is kinetic or all is potential.
Find the spring constant k, using your angular frequency and the mass.
Find the maximum potential energy.
Find the maximum kinetic energy.
Are they the same?
d. When the mass is located at one half its amplitude show that the potential energy is ¼ of the total energy.
e. Indicate in the figure on the left at what position(s) the force exerted on the mass is the most negative.
Phys223Exam 2 RedoName: ______
Score: ______
Indicate here at what times the force is the most negative. Is it consistent with the figure on the left?
Phys223Exam 2 RedoName: ______
Score: ______
Find the magnitude of the force in two different ways.
1. Use Hooke’s law:
2. Use the equation for the acceleration and Newton’s 2nd law:
f. The diagram below shows the extreme points of the oscillation. Use your equations from parts a and b to find the mass’s position, velocity and acceleration at t=1s.
x(t=1s)=
v(t=1s)=
a(t=1s)=
Sketch in the graph at the bottom the location and velocity of the mass at t=1s. Make sure your answer is consistent with your answers above.
For the same time, sketch the phase in the diagram for the corresponding CCW circular motion.Make sure your answer reflects the correct position and velocity.
g. Suppose now that the system is experiences small damping (damping force ~v, as done in class). Explain why is smaller than before but stays constant with time.
Problem 4
Phy203Quiz 2Name: ______
Score: ______
The 20 cm long wrench shown swings on its hook with a period of 0.90s. When the wrench hangs from a spring of spring constant 360 N/m, it stretches the spring 3.0cm.
Phys223Exam 2Name: ______
Score: ______
a. Find the mass of the wrench.
b. Draw a FBD of the wrench as shown in the figure. Include .
c. Use Newton’s 2nd law for rotational dynamics to set up the differential equation for . Use the small angle approximation .
d. Find the angular frequency(use the period).
e. What is the wrench’s moment of inertia about the hook?
f. What is the wrench’s moment of inertia about its center of mass?