Two charges are placed on the x axis. One of the charges (q1 = +6.23C) is at x1 = +3.00 cm and the other (q2 = -29.4C) is at x2 = +9.00 cm. Find the net electric field (magnitude and direction given as a plus or minus sign) at (a) x = 0 cm and (b) x = +6.00 cm.

2 kg of iron ingot at 1100^oC is mixed with 1 kg of water at -20^oC. Once the thermal equilibrium is reached, what would be the final state of water? Be as detailed as possible.

Mount Alberta in Jasper National Park, Alberta, has an elevation of 3620 m above sea level. Determine the atmospheric pressure at the top of Mount Alberta, assuming a sea level pressure of 101 kPa and a temperature of 12°C. (Consider that the average molar mass of air is 29 g/mol.)

A small block with mass 0.0400 kg is moving in the xy-plane. The net force on the block is described by the potential- energy function U(x,y)= (5.90 J/m2 )x2-(3.50 J/m3 )y3.

A)

What is the magnitude of the acceleration of the block when it is at the point x= 0.39 m , y= 0.68 m ?

Express your answer with the appropriate units.

B) What is the direction of the acceleration of the block when it is at the point x= 0.39 m , y= 0.68 m ?

A manufacturing plant uses 2.49 kW of electric power provided by a 60.0 Hz ac generator with an rms voltage of 470 V . The plant uses this power to run a number of high-inductance electric motors. The plant's total resistance is R = 30.0 Ω and its inductive reactance is XL = 42.0 Ω .

A) What is the total impedance of the plant?

B) What is the plant's power factor?

C) What is the rms current used by the plant?

D) What capacitance, connected in series with the power line, will increase the plant's power factor to unity?

E) If the power factor is unity, how much current is needed to provide the 2.49 kW of power needed by the plant?

F) Compare the current found in part E with the current found in part C. (Because power-line losses are proportional to the square of the current, a utility company will charge an industrial user with a low power factor a higher rate per kWh than a company with a power factor close to unity.)

A fireworks rocket is launched vertically upward at 40 m/s. At the peak of its trajectory, it explodes into two equal-mass fragments. One reaches the ground t1 = 2.63s after the explosion. When does the second fragment reach the ground?

1. If you have a cube of air exactly 1 cubic meter in volume at 25°C and atmospheric pressure,
   1. How much does it weigh (absolute weight, don’t worry about impact of surrounding air) in units of lbmass and N?
   2. If the air is cooled to 10°C, what happens to my cube?

Given a 2.00 μF capacitor, a 5.00 μF capacitor, and a 6.50 V battery, find the charge on each capacitor if you connect them in the following ways.

(a) in series across the battery

(b) in parallel across the battery

The figure shows an initially stationary block of mass m on a floor. A force of magnitude 0.500mg is then applied at upward angle ? = 20

The lob in tennis is an effective tactic when your opponent is near the net. It consists of lofting the ball over his head, forcing him to move quickly away from the net (see the drawing). Suppose that you loft the ball with an initial speed of 15.0 m/s at an angle of 50.0° the horizontal. At this instant your opponent is 10.0 m away from the ball. He begins moving away from you 0.41 s later, hoping to reach the ball and hit it back at the moment that it is 2.10 m above its launch point. With what minimum average speed must he move? (Ignore the fact that he can stretch, so that his racket can reach the ball before he does.)

• Construct a capacitor by filling a paper cup with water. What is the analog of voltage in this case, and what is the capacitance?
• Poke a small hole on the side of the paper cup near the bottom and let the water drain. How is this similar to an RC circuit?
• Decrease the R by making the hole slightly larger in diameter and re-run the demonstration. How is the rate of water flow consistent with the new RC value?
• Time how long it takes the cup to drain in each case and estimate the drainage rate (ounces or milliliters per second), make note of it, and compare the two.

A person standing on the ground is holding a spinning bicycle wheel. he reaches up and causes it to stop. Draw an angular momentum bar chart for the system of the person and the wheel. Comment on what provides any torques involved.

A parallel-plate capacitor has capacitance 8.00 μF. (a) How much energy is stored in the capacitor if it is connected to a 13.00-V battery? μJ (b) If the battery is disconnected and the distance between the charged plates doubled, what is the energy stored? μJ (c) The battery is subsequently reattached to the capacitor, but the plate separation remains as in part (b). How much energy is stored? μJ

A 1.78-kg block slides with a speed of 0.955 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 660 N/m. The block comes to rest after compressing the spring 4.18 cm.

Calculate the spring potential energy for a compression of 0 cm.

Calculate the kinetic energy of the block for a compression of 0 cm.

Calculate the total mechanical energy of the system for a compression of 0 cm.

Calculate the spring potential energy for a compression of 1.35 cm.

Calculate the kinetic energy of the block for a compression of 1.35 cm.

Calculate the total mechanical energy of the system for a compression of 1.35 cm.

Calculate the spring potential energy for a compression of 3.35 cm.

Calculate the kinetic energy of the block for a compression of 3.35 cm.

Calculate the total mechanical energy of the system for a compression of 3.35 cm.

You wire a real battery to a R1 = 42 Ω resistor and find that the output voltage between its terminals is V1 = 8.6 V. You disconnect it from the first resistor, wire it to a R2 = 720 Ω resistor, and find that its output voltage is V2 = 9.7 V. (a) Determine the current through each resistor. I1 = I2= (b) Find the internal resistance and emf of the battery. r = Ω e m f = V