You're considering installing a 4-foot-high by 8-foot-wide picture window in a north-facing wall (no solar gain) that now has a total R (specific thickness of material) value of 23. As a compromise between initial cost and energy savings, you've chosen a standard double-glazed window with the value of R is 2.0. As a result of installing this window, how much more oil will you burn in a 6-month winter heating season with an average outdoor temperature of 25F and an indoor temperature of 68F? Assume your oil furnace is 80% efficient.

A 5.4-µC point charge is located at x = 1.1 m, y = 2.9 m, and a -4.3-µC point charge is located at x = 2.3 m, y = -1.9 m.

(a) Find the magnitude and direction of the electric field at x = -2.7 m, y = 1.2 m.

(b) Find the magnitude and direction of the force on a proton at x = -2.7 m, y = 1.2 m.

Suppose the water at the top of Niagara Falls has a horizontal speed of 1.20 m/s just before it cascades over the edge of the falls. At what vertical distance below the edge does the velocity vector of the water point downward at a 47.3 ° angle below the horizontal?

In one model of the hydrogen atom, an electron orbits a proton in a circle of radius 5.28×10^-11 m with a speed of 2.18×10⁶ m/s. What is the acceleration of the electron in this model?

What is the period of the motion?

Option 1 – How We Hear This activity explores how we hear and how the physical nature of the sound wave determines the quality of the sound experience. Structure of the Ear What are the three main regions of the ear and their associated parts? Briefly describe what happens inside the cochlea? Sound Waves & Frequency What are the three aspects of sound waves? Briefly describe each aspect. Which type of tuning fork would vibrate faster—a small, short one or a large, long one? How is frequency measured and calculated? Explain why longer sound waves lead to lower frequencies and why shorter sound waves lead to higher frequencies. The Theory of Sound Briefly describe the three theories relating to how we perceive pitch. Explain why no single theory can explain human perception of pitch from 20 to 20,000 Hz.

I take my dogs on an afternoon walk. We leave my house, walking due East for 4 km. We then walk 3.5 km at an angle of 35 degrees West of North. Finally, we ealk 5.4 km at an angle of 15 degrees West of South. If I were to walk along a straight path that wuld take us back to my house, how far and in what direction should I walk?

You push a small mass (with respect to your mass) crate on a frictionless surface and it has some acceleration. If you are standing on the same frictionless surface, what happens to you?

Two solid bodies at initial temperatures T1 and T2, with T1 > T2, are placed in thermal contact with each other. The bodies exchange heat only with eachother but not with the environment. The heat capacities C ≡ Q/∆T of each body are denoted C1 and C2, and are assumed to be positive.

(a) Is there any work done on the system? What is the total heat absorbed by the system? Does the internal energy of each subsystem U1 and U2 change? What about the total internal energy U = U1 + U2?

(b) Calculate the final temperature, Tf , of the system.

(c) Show that T1 > Tf > T2.

(d) With the result of part (b), discuss what happens if C1 = 0 or C2 = 0. What about if C1 → ∞ or C2 → ∞? Interpret your results

One end of a very long wire is rigidly fastened to a post. The other end is attached to an audio speaker which shakes the end of the wire in a direction perpendicular to its length. The wire has a diameter 1.1 mm , a volume mass density of 7800 kg/m³, and is held under a tension of 6.7 N. The speaker creates a wave on the wire with an amplitude 0.56 cm and a frequency of 65.0 Hz .

Part A: Ignoring any reflections of the wave from the post, how much power is transferred from the speaker to the wave?

P = _______________W

Part B: If I double the frequency at which the speaker oscillates, while keeping the power output the same, what is the new amplitude of the wave?   

A = ____________cm

A person in a canoe can paddle his canoe at a steady 3.0 m/s in still water. He wishes to cross a 2.4 km wide river that has a current of 1.8 m/s traveling in the northward direction. Give step by step details in your solutions and solve graphically and analytically.

A) If this person first aims his canoe straight across the river in the eastern direction, the current will carry him downstream as he paddles across. What will be his actual velocity (magnitude and angle with respect to the eastward diredction) as he crosses? How long will it take him to cross the river?

B) If he aims the canoe somewhat upstream, he can actually travel straight across the river. In what direction must he aim? What is his actual speed across the river for this situation, and how long will it take him to cross? (Hint: The downstream direction found in part (a) will not be the same as the upstream angle required in part b!) (Hint: You will need a compass for the graphical method)

A trebuchet was a hurling machine built to attack the walls of a castle under siege. A large stone could be hurled against a wall to break apart the wall. The machine was not placed near the wall because then arrows could reach it from the castle wall. Instead, it was positioned so that the stone hit the wall during the second half of its flight. Suppose a stone is launched with a speed of v₀ = 25.0 m/s and at an angle of θ₀ = 41.0°. What is the speed of the stone if it hits the wall (a) just as it reaches the top of its parabolic path and (b) when it has descended to half that height? (c) As a percentage, how much faster is it moving in part (b) than in part (a)?

A truck traveling at a constant speed of 28 m/s passes a more slowly moving car. The instant the truck passes the car, the car begins to accelerate at a constant rate of 1.2 m/s^2 and passes the truck 545 m farther down the road. What was the speed of the car (in meters/second) when it was first passed by the truck?

A 10-cm-long thin glass rod uniformly charged to 15.0 nC and a 10-cm-long thin plastic rod uniformly charged to - 15.0 nC are placed side by side, 4.30 cm apart. What are the electric field strengths E1to E3 at distances 1.0 cm, 2.0 cm, and 3.0 cm from the glass rod along the line connecting the midpoints of the two rods?

Part A

Specify the electric field strength E1

Express your answer with the appropriate units.

Part B

Specify the electric field strength E2

Express your answer with the appropriate units.

Part C

Specify the electric field strength E3

Express your answer with the appropriate units.

23) In a 5000 m race, the athletes run 1212 laps; each lap is 400 m. Kara runs the race at a constant pace and finishes in 17.9 min. Hannah runs the race in a blistering 15.3 min, so fast that she actually passes Kara during the race.

How many laps has Hannah run when she passes Kara?​