Problem 3

Police car is chasing a speed limit violator car with a Doppler radar installed on the roof. Suppose the speed of sound is 300 m/s. When the police car has a velocity v = 10 m/s in the lab frame, it sends a 30 kHz frequency signal.

3.1 If the violator is moving at 20 m/s, what would be the frequency of the radar signal if received by an instrument installed at the violator car?

3.2 If the police car detected a returning signal at 29 kHz (after bouncing off the violator’s car), what is the velocity of the violator? Describe the situation in words.

Suppose we took a parallel plates capacitor: the plates have area 1 by 1 meter and they are separated by 1 cm with vacuum.

3.3 What would be the force between the two plates if we deposit a charge of 1 Coulomb.

3.4 How will the force in 3.3 change if we fill the space between the capacitors plate with a silicon, which has a dielectric relative permittivity of 10.

Suppose we have made a different capacitor, which consists of two oppositely charged small spheres with a radius R separated by a distance D. Assume R << D and the charge is distributed uniformly on the surface of the sphere. Consider an X-axis originating in the center of the first sphere and going through the center of the second sphere. The two centers are at X = 0 and X =D.

3.5 Sketch the electric field between X = R and X = D-R.

3.6 If once the sphere is given a charge Q and the other –Q, calculate the voltage difference between the two spheres.

3.7 Calculate the capacitance and express it via R, D, and epsilon_0.

An inertial reference system S' moves in the x-direction at speed υ relative to reference system S. The axis x’ slides along the x axis. Considering a uniform electric field in the region between the plates of a large parallel plate capacitor moving with S'. Show that the component of electric field E parallel to the motion is unchanged, that is, Ex = Ex’. [

An electron (q=-1.602x10^(-19)C and m=9.11x10^(-31)kg) is place at the center of an infinite uniformly charged cylinder (ρ=-0.15µC/m^(3)and radius of 5cm) with a speed of 3.2Mm/s radially outward. What is the speed of the electron after it moves 10m? Assume it doesn't hit everything.

Suppose heat is transferred at a rate of 500 W into 1 L of water. The water starts at 20˚C.

a) How much heat is required to raise the water temperature to 100 ˚C? How long does this take?

b) How much heat is required to boil off half the water? How long does this take? Comment on the value compared to part a.

c) Plot temperature vs Q for this heating process. You should only need 3 points for the graph, connected by straight lines. You should have this information from the previous steps.

I am taking physics lab and I can not understand the difference of the sources of errors below:

Random error in measurement

Random intrinsic error

Systematic error in measurement

Systematic intrinsic error

So, can you explain the difference between them please

A 2.20-m radius playground merry-go-round has a mass of 101.5 kg and is rotating with an angular velocity of 0.91 rev/s. What is its angular velocity after a 38.4-kg child gets onto it by grabbing its outer edge? The child is initially at rest. Express your answer in revs/s.

A series of whole-body counts indicated that a worker had a body burden of 18 microCi of Na-24 which was cleared from his body with effective half-life of 12 hours. Calculate: a. The biological half-life b. Cumulative activity c. Dose to the whole body

a) What is the greatest possible geocentric latitude of Venus, i.e., how far from the Sun can the planet be at the inferior conjunction? Assume the orbits are circular. b) When is the situation possible? The longitude of the ascending node of Venus is 77◦ .

A uniform plank of mass M and length L leans against a vertical wall. The initial angle it makes with the horizontal ground is 60º. It is let go from rest and slides down frictionlessly. The moment it leaves contact with the wall, what angle does it make with the ground? There is no friction anywhere.

A heat engine uses a heat source at 580 ∘C and has an ideal (Carnot) efficiency of 29 % .

To increase the ideal efficiency to 46 % , what must be the temperature of the heat source?

Is work done when dragging a mass up a hill the same as the change in potential energy?

Is work the same as energy? I am confused as to why

The pV diagram in (Figure 1) shows a cycle of a heat engine that uses 0.250 mole of an ideal gas having γ=1.10. The curved part ab of the cycle is adiabatic. The internal energy of the gas changes by the following amounts: ΔUa→b=−2220J, ΔUb→c=−1.06×104J, and ΔUc→a=+1.29×104J. c=(0.002, 1.5) b=(0.009, 1.5)

Part A: Find the pressure of the gas at point a.

Express answers in pascals to three significant figures.

Part B: How much heat enters this gas per cycle?

Express your answer in joules to three significant figures.

Part D: How much heat leaves this gas in a cycle?

Express your answer in joules to three significant figures.

Part F: How much work does this engine do in a cycle?

Express your answer in joules to three significant figures.