Capacitors won't hold a charge indefinitely; as time goes on, charge gradually migrates from the positive to the negative plate. We can model this as a discharge of the capacitor through an internal "leakage resistance." A 0.49F capacitor charged to 3.7V will initially discharge with a leakage current of 0.25mA .

I found the leakage resistance to be 1.5

Question 1: Answer, True or False

The index of refraction has units of distance.

True

False

When we make multiple measurements, we can have more confidence in the index of refraction determination.

True

False

Glass is more dense than water.

True

False

It is possible to exceed the speed of light in a vacuum

True

False

A tangent line is parallel to a normal line

True

False

The index of refraction is unitless.

True

False

There is a special case when the index of refraction is less than 1.

True

False

3. Work is inputted to isothermally move a 1500 Kg mass from an elevation of zero to 35m and to change it velocity. The initial velocity of the mass is 0.55 m/s. The drag work for this process is described by a force which varies over the distance travel, F = ax + b; where F is in Newtons, the coefficient (a) has units of N/m and the constant (b) has units of N. For this application a = 4.1 N/m and b = 700 N. The force is applied over a distance of 1730 m. There is a heat loss from friction of 1.1(106 ) J during this process. Determine the final velocity of the mass.

3b. The input work for this process is from a combustion engine that has an efficiency of 0.28. The heating value of the fuel is 30.0 MJ/liters and its cost is $0.83/liter. Determine the volume of fuel required and its cost to perform the process described in (3.).

Please solve with sketches and clear equations. Thanks!

What is the intensity in W/m² of a laser beam used to burn away cancerous tissue that, when 93.5% absorbed, puts 493 J of energy into a circular spot 2.13 mm in diameter in 3.70 s?

_______________W/m²

How many times more intense is this than the maximum intensity of direct sunlight (about 1360 W/m²)?

_______________

In a pool game, the cue ball, which has an initial speed of 7.0 m/s, make an elastic collision with the eight ball, which is initially at rest. After the collision, the eight ball moves at an angle of 25° to the original direction of the cue ball.

(a) Find the direction of motion of the cue ball after the collision (______) I got the 60° which is right.

(b) Find the speed of each ball. Assume that the balls have equal mass.

(_____m/s)

(_____m/s)

A cylindrical specimen of a brass alloy 8.3 mm (0.33 in.) in diameter and 76.7 mm (3.02 in.) long is pulled in tension with a force of 7360 N (1655 lbf); the force is subsequently released.
(a) Compute the final length of the specimen at this time. The tensile stress-strain behavior for this alloy is shown in Animated Figure 7.12.
(b) Compute the final specimen length when the load is increased to 20300 N (4563 lbf) and then released.

A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 83.2 N at an angle of 28.0° above the horizontal. The box has a mass of 20.0 kg, and the coefficient of kinetic friction between box and floor is 0.300. (Indicate the direction with the sign of your answer.)

(a) Find the acceleration of the box. (Assume that the +x-axis is to the right and the +y-axis is up along the page.)

(b) The student now starts moving the box up a 10.0° incline, keeping her 83.2 N force directed at 28.0° above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box? (Assume that the +x-axis is along the incline and the +y-axis is upwards and perpendicular to the incline.)

PLEASE EXPLAIN STEPS

A long solenoid has 110 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.50 cm perpendicular to the solenoid axis. The speed of the electron is 0.040 c (c = speed of light). Find the current i in the solenoid.

An object (A) of mass m A = 28.0 kg is moving in a direction that makes angle of 50° south of west with a speed v A = 4.90 m/s, while object (B) of mass m B = 18.0 kg is moving due south with a speed v B = 7.85 m/s. The two objects collide and stick together in a completely inelastic collision. Find the magnitude of the final velocity of the two-object system after the collision.

two happy astronaunts, each having a mass of 75 kg are connected by a rod length 10.0 and a mass 140 kg. The system is isolated in space, orbiting the center of the rod at an angular speed of 0.50 rad/s counterclockwise. Treat the astronaunts as point masses. The moment of inertia of a rod is I=(1/12)ML^2

what is the initial moment of intertia of the total rod-and-astronaunts system?

By pullinh on the rod, the astronaunts shorten the distance between them to 5.0 m. What is the final angular velocity of the rod-and-astronauts system in rad/s?

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.