Exercise 1.40
You are given two vectors A⃗ =−3.00ι^+6.00j^and B⃗ =4.00ι^+2.00j^. Let the counterclockwise angles be positive.
Part A
What angle does A⃗  make with the +x-axis?

θ1=
∘

SubmitMy AnswersGive Up
Part B
What angle does B⃗  make with the +x-axis?

θ2=
∘

SubmitMy AnswersGive Up
Part C
Vector C⃗  is the sum of A⃗  and B⃗ , so C⃗ =A⃗ +B⃗ . What angle does C⃗ make with the +x-axis?

θ3=

a. Assume that all of the pendulum’s mass M is contained in the “bob” at the end of the pendulum rod. Write Newton’s 2nd Law for the force balance along the circular arc traced out by the pendulum bob as it swings back and forth. [Hint: You can relate the position of the pendulum bob along its arc to the angle ! formed by the pendulum rod and the vertical line when the pendulum bob is at the “base” of the arc. It may help to draw this.]

b. Using the “small angle approximation” sin(theta) ≈ theta(t) and assuming that the pendulum bob is released from rest at an angle theta(zero), show that theta(zero) = (theta(zero))cos (omega t) solves the force balance equation in (a) for a particular value of omega. What value is it?

c.  The period of the pendulum corresponds to the time it takes the pendulum to oscillate through one cycle, i.e., from its initial position and back. Use the result in b to find the period. You should find the period to be a numerical factor times our estimate of the period from dimensional considerations.

Table 1                              
                              
   DATA               CALCULATIONS          
L (mm)   Rrm (Ω)   ΔL (mm)   Rhot (Ω)   Trm (C°)   Thot (C°)   ΔT (C°)  
Copper 699   112 0.79 9.2 22.5   84.75 62.25  
Steel 699   112 0.64 9.437 22.5   84 61.5  
Aluminum 699   112 1.07 9.767 22.5   83 60.5  
                              
1. Use the Conversion Table at the end of the 'Instructions' section, or the one on the top of the expansion base, to convert your thermistor resistance measurements, Rrm and Rhot, into temperature measurements, Trm and Thot. Record your results in the table.                                
                              
                              
     2. Calculate ΔT = Thot – Trm. Record the result in the table.                              
                              
3. Using the equation ΔL = αL ΔT, calculate α for copper, steel, and aluminum.                              
                              
αCu =   1.81556E-05               αsteel =   1.48877E-05      
                              
αAl =   2.53018E-05                          

1. Look up the accepted values for the linear expansion coefficient for copper, steel, and aluminum. Compare these values with your experimental values. What is the percentage difference in each case? Is your experimental error consistently high or low?                                
                              
   2. On the basis of your answers in question 1, speculate on the possible sources of error in your experiment. How might you improve the accuracy of the experiment?                               
                              
                              

       3. From your result, can you calculate the coefficients of volume expansion for copper, aluminum, and steel? (i.e. ΔV = αvol V ΔT)                                
                              
                              

You place your lunch leftovers in the refrigerator. Suppose the refrigerator needs to remove 2.0090E+4 J of thermal energy from your lunch to cool it to the temperature of the inside of the refrigerator. In the meantime, this means the refrigerator produces 2.7959E+4 J of thermal energy that it expels into the kitchen as a result. What is the total work done by the compressor motor in the refrigerator? (Ignore any thermal loses due to friction in the motor.)

What is the Coefficient of Performance for the refrigerator?

Your refrigerator actually acts like a heater in your kitchen. Suppose you have a small electric space heater that has a power output of 1.2kW. How long would this heater have to run to produce the same amount of heat as the refrigerator produced while cooling your leftovers?

It takes electricity to run the motor on the refrigerator. If your cost of electricity is 13 cents per kilowatt*hour, how much does it cost (in cents - do not enter units) to cool your lunch down?

A) What should his speed be at the top of the ramp to make it to the edge of the bank? B) if his speed was half the value found in part A where would he land?  A physics professor did daredevil stunts in his spare time. His last stunt was an attempt to jump across a river on a motorcycle (the figure (Figure 1) ). The takeoff ramp was inclined at 53.0 ?, the river was 40.0 m wide, and the far bank was 15.0 m lower than the top of the ramp. The river itself was 100 m below the ramp. You can ignore air resistance.

A lidar (laser radar) gun is an alternative to the standard radar gun that uses the Doppler effect to catch speeders. A lidar gun uses an infrared laser and emits a precisely times series of pulses of infrared electromagnetic waves. The time for each pulse to travel to the speeding vehicle and return to the gun is measured. In one situation a lidar gun in a stationary police car observes a difference of 1.23 10-7 s in round-trip times for two pulses that are emitted 0.440 s apart. Assuming that the speeding vehicle is approaching the police car essentially head-on, determine the speed of the vehicle.

By what factor must your blood pressure increase to compensate for a 4 % narrowing in your blood vessels? (The pressure difference across your blood vessels is essentially equal to your blood pressure.) I am learning the bernoullis equation and also the poiseuille law. But can't figure out how to do this with only knowing a percent. I need each step please.

The very long cylindrical solenoid of (Figure 1) has a radius of 0.50 m and 1000 windings per meter along its length. A circular conducting loop of radius 1.0 m encircles the solenoid, with the long central axis of the solenoid passing through the center of the loop, and with the area vector of the loop parallel to the solenoid axis. The solenoid initially carries a steady current I, but the current is then reduced to zero during a 0.100-s time interval.

Part A

If the average emf induced in the loop during that interval is 0.80 V , what was the initial current magnitude?

An electron is constrained to the central perpendicular axis of a ring of charge of radius 2.3 m and charge 0.020 mC. Suppose the electron is released from rest a distance 0.056 m from the ring center. It then oscillates through the ring center. Calculate its period. (The electron is always much closer to the ring center than a radius.)

A piston-cylinder device contains 0.5 m³ air at 100 kPa and 1000 K. Because the outside is cooler (at 300 K), the hot air starts losing heat to the surroundings and the volume of air starts decreasing. Over a certain period of time the volume is observed to shrink by 50%.

The final temperature is lower or higher?

Determine the boundary work transfer (absolute value). in KJ

Two capacitors C₁ = 4.6 ?F, C₂ = 18.6 ?F are charged individually to V₁ = 15.3 V, V₂ = 4.4 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.
Calculate the final potential difference across the plates of the capacitors once they are connected.

Calculate the amount of charge (absolute value) that flows from one capacitor to the other when the capacitors are connected together.

By how much (absolute value) is the total stored energy reduced when the two capacitors are connected?

I am wondering whether the five1 units of the natural unit system really is dictated by nature, or invented to satisfy the limited mind of man? Is the number of linearly independent units a property of the nature, or can we use any number we like? If it truly is a property of nature, what is the number? -five? can we prove that there not is more?

In the answers please do not consider cgs units, as extensions really is needed to cover all phenomenon. - or atomic units where units only disappear out of convenience. - or SI units where e.g. the mole for substance amount is just as crazy as say some invented unit to measure amount of money.

Sound source A is located at x = 0, y = 0, and sound source B is located at x = 0, y = 2.0 m. The two sources radiate coherently and in phase. An observer at x = 15.8 m, y = 0 notes that as he takes a few steps from y = 0 in either the +yor −y-direction, the sound intensity diminishes. What is the lowest frequency, and the next to the lowest frequency of the sources that can account for that observation? (Enter your answers from smallest to largest.)

kHz

kHz

a) What are the different types of “light” (electromagnetic waves), starting from radio waves? Why do you think we can only see such a small portion of the electromagnetic spectrum? Why don’t we see X-rays or microwaves?

b) Explain what a photon is and what property of photons relates to different colors of light.

c) What is the frequency of light that has a wavelength of 400 nm? What is the color of such light? What is the energy of a photon of such light (in eVunits)?