If a fish is attached to a vertical spring and slowly lowered to its equilibrium position, it is found to stretch the spring by an amount d. If the same fish is attached to the end of the unstretched spring and then allowed to fall from rest, through what maximum distance does it stretch the spring? (Hint: Calculate the force constant of the spring in terms of the distance d and the mass m of the fish.)

/0 Comments/in /by

If a fish is attached to a vertical spring and slowly lowered to its equilibrium position, it is found to stretch the spring by an amount d.
If the same fish is attached to the end of the unstretched spring and then allowed to fall from rest, through what maximum distance does it stretch the spring? (Hint: Calculate the force constant of the spring in terms of the distance d and the mass m of the fish.)
Express your answer in terms of d.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. There is no one around to help, so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. You pull up on the rope to lift the box. (Figure 1) Use g for the magnitude of the acceleration due to gravity and neglect friction forces. Part A Once you have pulled hard enough to start the box moving upward, what is the magnitude F of the upward force you must apply to the rope to start raising the box with constant velocity?

/0 Comments/in /by

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. There is no one around to help, so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. You pull up on the rope to lift the box.
(Figure 1)
Use g for the magnitude of the acceleration due to gravity and neglect friction forces.
Part A Once you have pulled hard enough to start the box moving upward, what is the magnitude F of the upward force you must apply to the rope to start raising the box with constant velocity?
Express the magnitude of the force in terms of m, the mass of the box.
Part BConsider lifting a box of mass mto a height husing two different methods: lifting the box directly or liftingthe box using a pulley (as in the previous part).
What is {W_{rm d}}/{W_{rm p}}, the ratio of the work done lifting the box directly to the work done lifting the box with a pulley?
Express the ratio numerically.

While a roofer is working on a roof that slants at 41.0 ∘ above the horizontal, he accidentally nudges his 95.0 N tool box, causing it to start sliding downward, starting from rest. Part A If it starts 5.00 m from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 21.0 N?

/0 Comments/in /by

While a roofer is working on a roof that slants at 41.0 ∘ above the horizontal, he accidentally nudges his 95.0 N tool box, causing it to start sliding downward, starting from rest.
Part A If it starts 5.00 m from the lower edge of the roof, how fast will the toolbox be moving just as it reaches the edge of the roof if the kinetic friction force on it is 21.0 N?
A force parallel to the x-axis acts on a particle moving along the x-axis. This force produces a potential energy U(x) given by U(x)=α x4where α=1.16 J/m4 .
Part A What is the force when the particle is at position x = -0.660 m ?

Question-1. A box of mass m is sliding along a horizontal surface. Part A The box leaves position x=0 with speed v0. The box is slowed by a constant frictional force until it comes to rest at position x=x1. Find the magnitude of the average frictional force that acts on the box. (Since you don't know the coefficient of friction, don't include it in your answer.)Express the frictional force in terms of m, v0, x1

/0 Comments/in /by

Question-1. A box of mass m is sliding along a horizontal surface.
Part A The box leaves position x=0 with speed v0. The box is slowed by a constant frictional force until it comes to rest at position x=x1.
Find the magnitude of the average frictional force that acts on the box. (Since you don’t know the coefficient of friction, don’t include it in your answer.)Express the frictional force in terms of m, v0, x1
Part B After the box comes to rest at position x1, a person starts pushing the box, giving it a speed v1.
When the box reaches position x2(wherex2 > x1), how much work has the person done on the box? Assume that the box reaches x2 after the person has accelerated it from rest to speedv1.Express the work in terms of m, v0, x1, x2, v1

Analyze the circuit below using a QCV chart. You must show appropriate work for full credit. 2) Analyze the circuit below using a QCV chart. You must show appropriate work for full credit. 3) Analyze the circuit below using a QCV chart. You must show appropriate work for full credit. 4) An Oppo Digital Blu-Ray player [DMP-95] (Yes, I am an audiophile.) has a power cable which has a metal that allows 9 x 1019 electrons per cubic millimeter. On average, the cable passes 1 x 1022 electrons every hour. The electrons passing through the player have a drift velocity of 4.5 μm/s. (a) What current does the Oppo draw? (b) Calculate the diameter of the cable?

/0 Comments/in /by

Analyze the circuit below using a QCV chart. You must
show appropriate work for full credit. 2) Analyze the circuit below using a QCV chart. You must
show appropriate work for full credit. 3) Analyze the circuit below using a QCV chart. You must
show appropriate work for full credit. 4)
An Oppo Digital Blu-Ray player [DMP-95] (Yes, I am an audiophile.) has a power cable which has a metal that allows 9 x 1019 electrons per cubic millimeter. On average, the cable passes 1 x 1022 electrons every hour. The electrons passing through the player have a drift velocity of 4.5 μm/s. (a) What current does the Oppo draw? (b) Calculate the diameter of the cable?
5) The Large Hadron Collider at CERN creates proton beams which collide together resulting in pictures like the one at the right. Some of these beams can have a radius of 1.1 mm with a current of 1.5 mA. The kinetic energy of each proton in this beam is 2.5 MeV. (a) Calculate the number density of the protons in the beam. (b) If the beam is aimed at a metal target, how many protons would strike the screen in 1 minute?
C2 = 15 μF C1 = 8 μF
20 V
C3 = 30 μF
6)
Two copper wires are soldered together. Wire #1 has a radius of 0.7 mm. Wire #2 has a radius of 1.2 mm. Copper has a number density of 8.47 x 1028 e–/m3. The drift velocity in Wire #1 is 0.72 mm/s. If you want the current to remain the same in both, what is the drift velocity in Wire #2?
7) A nichrome cable has a current of 140 A running through
it. Between two points on the cable that are 0.22 m apart, there is a potential difference of 0.036 V (a) Calculate the diameter of the cable. (b) How much heat energy does this part of the wire emit in 1 minute?
8) A “Rockstar” toaster uses a
tungsten heating element (wire). The wire has a diameter of 1.2 mm. When the toaster is turned on at 20° C, the initial current is 1.6 A. (a) What is the current density in the wire? (b) A few seconds later, the toaster heats up and the current is 1.20 A. What is the temperature of the wire? (c) If the toaster is plugged into a standard wall outlet in Kankakee, Illinois, what is the rate that energy is dissipated from the heating element?
9) Skid runs a 10 mile line of copper cable out to his shack in
the sticks so he can have electricity to play Lord of the Rings Online. At 20ºC the resistance of the cable is 12 Ω. At 50ºC the cable emits 1.5 kJ every second. (a) What is the resistance of the cable at 50ºC? (b) What is the current running through the cable at 50ºC? (c) Calculate the current density at 50ºC.
C1 = 18 μF
Wire #1 Wire #2 C2 = 6 μF
C3 = 4 μF
C4 = 30 μF 25 V
C1 = 5 μF C2 = 4 μF
C3 = 1 μF
C4 = 12 μF
15 V
10) A modern hair dryer uses a nichrome heating element that typically is 30-gauge wire around 40 cm in length. The gauge rating on a wire refers to its diameter. In this case, 30-gauge wire has a diameter of 0.254 mm. Nichrome has a number density of 7.94 x 1028 e–/m3. If the drift velocity of the electrons in the wire is 18.7 mm/s, what is the voltage that the hair dryer is plugged into?
11) Before LCD, LED, Plasma,
and (the latest) OLED TVs, there were CRT (Cathod-Ray Tube) TVs. Inside these TVs were electron guns that shot an electron beam of diameter 0.5 mm and current density of 244 A/m2 onto the inside of a glass screen which was coated with phosphor. How many electrons would hit the phosphor every minute?
12)
Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.
13)
Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.
14)
Determine the equivalent resistance between points A and B for the resistors shown in the circuit above.
15) Design a circuit that has an equivalent resistance of
1.00 Ω using at least one of each of the following resistors: a 1 Ω, a 2 Ω, and a 6 Ω. [You must also show where your A and B terminals are located.]

1) You have a parallel plate capacitor of plate separation 0.1 mm that is filled with a dielectric of neoprene rubber. The area of each plate is 1.8 cm2. (a) Calculate the capacitance of the capacitor. The capacitor is charged by taking electrons from one plate and depositing them on the other plate. You repeat this process until the potential difference between the plates is 350 V. (b) How many electrons have been transferred in order to accomplish this?

/0 Comments/in /by

1) You have a parallel plate capacitor of plate separation
0.1 mm that is filled with a dielectric of neoprene rubber. The area of each plate is 1.8 cm2. (a) Calculate the capacitance of the capacitor. The capacitor is charged by taking electrons from one plate and depositing them on the other plate. You repeat this process until the potential difference between the plates is 350 V. (b) How many electrons have been transferred in order to accomplish this?
2) A capacitor with ruby mica has an effective electric field
between the plates of 4600 V/m. The plates of the capacitor are separated by a distance of 4 mm. 50 mJ of energy is stored in the electric field. (a) What is the capacitance of the capacitor? (b) Calculate the energy density in between the plates.
3) A capacitor with a dielectric of paper is charged to 0.5 mC.
The plates of the capacitor are separated by a distance of 8 mm. 40 mJ of energy is stored in the electric field. (a) What is the strength of the effective electric field? (b) Calculate the energy density in between the plates.
4) A capacitor of 10 μF is charged by connecting it to a
battery of 20 V. The battery is removed and you pull the plates apart so that you triple the distance between them. How much work do you do to pull the plates apart?
5) The flash on a disposable camera contains a capacitor
of 65 μF. The capacitor has a charge of 0.6 m C stored on it. (a) Determine the energy that is used to produce a flash of light. (b) Assuming that the flash lasts for 6 ms, find the power of the flash. (Think back to 225.)
6) A spherical shell conductor of
radius B encloses another spherical shell conductor of radius A. They are charged with opposites signs but same magnitude, q. (a) Using integration, derive an equation for the capacitance of this spherical capacitor. (b) Calculate the capacitance if A = 45 mm and B = 50 mm. (c) If q = 40 μC, what is the energy density in between the shells?
7) You attach a battery of 15 V to an air-filled capacitor of 5 μF and let it charge up. (a) If the plate separation is 3 mm, what is the energy density in between the plates? You then remove the battery and attach the capacitor to a different uncharged capacitor of 2 μF. (b) What is the amount of charge on each capacitor after they come to equilibrium?
8) You attach a 100 pF capacitor to a battery of 10 V. You
attach a 250 pF to a battery of 7 V. You remove both of the batteries and attach the positive plate of one capacitor to the positive plate of the other. After they come to equilibrium, find the potential difference across each capacitor.
9) Do problem #8 but when you attach the capacitors
together attach the opposite sign plates instead of the same sign plates.
10)
Determine the equivalent capacitance between points A and B for the capacitors shown in the circuit above.
11)
4 μF
4 μF
6 μF
12 μF
30 μF
20 μF
A
B
75 μF
6 μF
12 μF
12 μF
18 μF
20 μF
A
B
Determine the equivalent capacitance between points A and B for the capacitors shown in the circuit above.
12) Design a circuit that has an equivalent capacitance of
1.50 μF using at least one of each of the following capacitors: a 1 μF, a 2 μF, and a 6 μF. [You must also show where your A and B terminals are located.]
13) The two capacitors above both have plates that are
squares of sides 3 cm. The plate separation is 1.2 cm for both. Between each of the capacitor plates are two different dielectrics of neoprene rubber and Bakelite. Everything is drawn to scale. Find the capacitance of each capacitor. (HINT: Think series and parallel.)
14) The plates of an air-filled capacitor have area, A, and are
separated by a distance, d. The capacitor is charged by a battery of voltage, V. Three things are going to change: (1) The plates of the capacitor are pulled apart so that the distance between the plates triples. (2) The area of the plates increase by a factor of 6. (3) The voltage of the battery decreases by a factor of 4. Determine expressions in terms of A, d, and/or V for (a) the new capacitance, (b) the new charge, and (c) the new energy density.
15)
A massless bar of length, L, is hanging from a string that is attached 1/3 of the length of the bar from the right end. A block of mass, M, is hung from the right end. The left end of the bar has an air-filled massless capacitor of plate area, A, and plate separation, d. Find an expression for the potential difference between the plates so that this system is in equilibrium. (HINT: You will
need the equation dx dU
F −= from 225.)