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?​

Explain in terms of the location of the center of mass, the physical reason why you begin to fall forward when you lean forward far enough.

Light from a fluorescent lamp is observed through a cloud of cool nitrogen gas. Again, two students are having a discussion about the kind of spectra that they would see.

Student 1: We would see absorption line spectra and the missing lines would correspond to the light from the fluorescent lamp.

Student 2: I disagree. We would see an emission line spectrum corresponding to nitrogen. This would happen because the nitrogen gas would absorb some energy from the fluorescent lamp and would reemit this energy which would result in an emission line spectrum.

**** Which student, if any, do you agree with and why?

The frequency of light reaching Earth from a particular galaxy is 18% lower than the frequency the light had when it was emitted. a) explain whether the galaxy is moving toward or away from earth. b) What is the speed of this galaxy relative to the Earth? Give your answer as a fraction of the speed of light.

10 kg crate is pulled 4.9 m up a 34 degree incline by a rope angled 16 degree above the incline. The tension in the rope is 125 N, and the crate's coefficient of kinetic friction on the incline is 0.26.
How much work is done by:
a. Tension? J

b. Gravity? J

c. Normal Force? J

d. What is the increase in thermal energy of the crate and incline?

J

1. (i)Use the Huygens principle to explain how plane parallel wavefronts are diffracted at a single aperture.

2. (ii) Use the principle of superposition to explain how coherent light emerging from two narrow slits can interfere to produce a pattern on a distant screen.

Why is that the masses for proton and neutron more precisely measured in atomic mass units (u) than in megaelectron volts (MeV)?