*Relativity and time - 1

The distance between New York and Los Angeles is about 5,000 km. A jet, traveling at a speed of 769 km/hour, leaves New York. Calculate the time elapse for the plane to reach the Los Angeles airport. Now calculate the difference in the time that has elapsed for an observor on earth and a passenger on the plane? Give your answers in nanoseconds (ns)

An AC generator supplies an rms voltage of 230 V at 60.0 Hz. It is connected in series with a 0.300 H inductor, a 4.30 μF capacitor and a 256 Ω resistor.

What is the impedance of the circuit?

What is the rms current through the resistor?

What is the average power dissipated in the circuit?

What is the peak current through the resistor?

What is the peak voltage across the inductor?

What is the peak voltage across the capacitor?

The generator frequency is now changed so that the circuit is in resonance.

What is that new (resonance) frequency?

after falling from rest from a height of 30 m, a 0.50 kg ball rebounds upward, reaching a height of 20 m. if the contact between bam and ground lasted 2.0 ms, what average force was exerted on the ball?

How do you use errors in mass and velocity to find the errors in starting and ending kinetic energy?

Equation for KE = 1/2mv^2

Error in m = 0.179kg +/- 0.005 kg

Error in velocity starting = -0.0648m/s +/- 0.011 m/s

Error in velocity ending = 0.259m/s +/- 0.020 m/s

Describe a method by which you can independently verify the uncertainty on your force measurements for the Acceleration of a Cart lab.\

Describe a method by which you can independently verify the uncertainty on your acceleration measurements for the Acceleration of a Cart lab.

At the x = 0 end of an semi-infinite rope, someone moves the end of the rope up and down sinusoidally as y[x = 0, t] = A Cos[ω t + π/4]: The speed of propagation down the string is given by c. (a) Write down a general formula for the resulting wave that propagates down the string. (b) What power is supplied by the person at the end of the rope? (c) At what frequencies ω must the person move the string so that at x = L the string moves with transverse harmonic motion given by y(x = L, t) = A Sin[ω t - π/4] ?

Classic footage of the Apollo 11 astronauts show them taking large leaps bounding around the surface of the moon. By transporting this simple spring and mass system to the moon, we can measure the gravitational force exerted by the moon on objects at its surface and compare it to the force of gravity exerted by the earth on people at its surface.

i. Use the apparatus to measure the force of gravity exerted by the moon on the 50 gram mass. What is the value of this force?
ii. If this mass is dropped from a height of 10 m, at what rate does this mass
accelerate towards the surface?
iii. If you can jump to a height of 2 feet on earth, explain using energy principles why the change in gravitational force enables you to jump much higher on the moon.

QUESTION 9

Tony Hawk is skating through a half-pipe with a radius of 4 m. Initially he is in a crouched position with his center of mass 0.5 m above the surface of the half-pipe. He starts from rest with his center of mass a height of 3 m above the base of the half-pipe and experiences no loss of energy from friction as he moves. At the bottom of the half-pipe he stands up and lifts his arms into the air, thereby raising his center of mass to 1.0 m. He then continues up the other side of the half-pipe. What is the maximum height (in m) that his center of mass reaches on the other side of the half-pipe? You may model Tony as a point particle.

A simple pendulum, 2.0 m in length, is released by a push when the support string is at an angle of 25° from the vertical. If the initial speed of the suspended mass is 3.0 m/s when at the release point, to what maximum angle will it move in the second half of its swing?

a. 47°

b. 36°

c. 30°

d. 19°

You are driving your car, and the traffic light ahead turns red. You apply the brakes for 2.73 s, and the velocity of the car decreases to + 5.37 m/s. The car’s deceleration has a magnitude of 3.02 m/s2 during this time. What is the car’s displacement? x =

A dynamite blast at a quarry launches a rock straight upward, and 1.8 s later it is rising at a rate of 10 m/s. Assuming air resistance has no effect on the rock, calculate its speed (a) at launch and (b) 4.4 s after launch.

Concept Simulation 2.3 provides some background for this problem. A ball is thrown vertically upward, which is the positive direction. A little later it returns to its point of release. The ball is in the air for a total time of 8.36 s. What is its initial velocity? Neglect air resistance. v0 =

Concept Simulation 2.3 offers a useful review of the concepts central to this problem. An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of +21.2 m/s and measures a time of 18.4 s before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet? (positive = up, negative = down)

A hot-air balloon is rising upward with a constant speed of 3.78 m/s. When the balloon is 9.24 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground? From her bedroom window a girl drops a water-filled balloon to the ground, 8.93 m below. If the balloon is released from rest, how long is it in the air?

From her bedroom window a girl drops a water-filled balloon to the ground, 8.93 m below. If the balloon is released from rest, how long is it in the air?

A shell is fired from a gun at an angle of 30 degrees to the horizon. The initial velocity of the shell is 10 m/s. What velocity will this shell have at a height of 2m? (Solve this problem by using kinematic equations)

1) Jason Statham jumps off of a diving board which is 3.0 m above the water surface. He lands traveling at 8.90 m/s at an angle of 75° with respect to the horizontal. (a) What was his initial take-off speed and direction? (b) Use the Order of Magnitude sense-making technique to check the validity of your answer to part (a).

2) An astronaut shipwrecked on a distant planet with unknown characteristics is on top of a cliff, which she wishes to descend. She does not know the acceleration due to gravity on the planet, and she has only a good watch with which to make measurements. She wants to learn the height of the cliff, and to do this she makes two measurements. First, she lets the rockfall from rest off the cliff edge; she finds that the rock takes 2.54 s to reach the distant ground below the cliff. Second, she releases the rock from the same spot but tosses it upward so that it rises 2 m before falling to the distant ground below the cliff; this time the rock takes 3.77 s to reach the ground. (a) What is the height of the cliff? (b) What planet in our solar system is this? (c) Use the Known Values sense-making technique to verify your answer to part (b).

3)While bowling, you throw the bowling ball forward down the right side of the lane. The ball has a constant forward velocity of 8.9 m/s. A bowling lane is 18.3 meters long and 1.05 meters wide. Since you are a professional bowler, you release the ball with a spin that causes the ball to accelerate to the left at a constant rate, a. To get a strike, you need your bowling ball to hit the headpin which is sitting at the end of the lane in the center. (a) What acceleration is needed to hit the headpin? (ignore the width of the pin and ball) (b) What is the final speed of the ball? (c) Use the Order of Magnitude sense-making technique to check the validity of your answer to part (b)

4) Gerry the gerbil walks 55 cm in the positive y-direction. After this, he is located 95 cm from the origin at an angle of 50° from the +xaxis towards the +y-axis, as shown in the figure. (a) Complete the figure by including the change in position and the initial position vectors. (b) Calculate Gerry’s initial position. (c) Use the Related Quantities sense-making technique to check the validity of your answer.

5) Deserted on a deserted Island you spot a slightly exposed tin can under a tree. Upon opening it you find it’s instructions to a treasure. It reads: “Ten paces from this very tree in a direction twenty degrees south of west lies the first location. Ten paces from this very tree in a direction sixty degrees north of east lie the second location. Walk from this tree exactly the distance and direction you would walk from the first location to the second location and you will find ye treasure. Yar” (a) What are the coordinates of treasure? (b) Use a physical representation in conjunction with the Related Quantities sense-making technique to check the validity of your answer.