A computer-controlled racecar is programmed to execute the following motion along the ground for 6.0 seconds. Let’s say the car begins at the origin of our coordinate system. Its initial velocity is ~v0 = (15:0 m/s)^i and its acceleration is constant: ~a = (?6:0 m/s2)^i + (?2:0 m/s2)^j

(a) Make a table, and calculate the car’s position vector, ~r at the end of each second, through t = 6:0 seconds. Use these data to plot the trajectory of the particle for this time interval. You can do it by hand on the axes given to you on the last page. (If you like, you could also do this by writing a computer program that would calculate hundreds of data points).

(b) On your graph, sketch vectors for both the car’s velocity and acceleration at t = 1:0; 2:0 and 4.0 seconds. At each of these instants, is the car speeding up or slowing down? How do you know?

(c) You may have found that judging the answer to part (b) was a tough call for t = 2:0 s. We can do this conclusively: i. Find both the velocity and the speed of the particle at t = 2:0 seconds. ii. At t = 2:0 seconds, find the rate at which the car’s speed is changing (Note that I’m not asking the rate at which its velocity is changing, which is just j~aj). (Hint: you’ll need to find the angle between ~v and ~a, which is something for which the vector dot product is very useful... ) iii. At what time is the rate of change of the car’s speed equal to zero, and what is the car’s speed at this instant? 3

(a)A cosmic ray proton streaks through the lab with velocity 0.82c at an angle of 52° with the +x direction (in the xy plane of the lab). Compute the magnitude and direction of the proton's velocity when viewed from frame S' moving with β = 0.74.

(b) Suzanne observes two light pulses to be emitted from the same location, but separated in time by 3.50 µs. Mark sees the emission of the same two pulses separated in time by 8.00µs.

How fast is Mark moving relative to Suzanne?c

According to Mark, what is the separation in space of the two pulses?

m

Two stars of equal mass orbit one another. (This is called a binary star system.) If the stars’ orbits have a semimajor axis of 2.5x10^8 km and complete one orbit every 2.4 years, what is the mass of each star? pick from: (8.1x10^29 kg, 1.6x10^30 kg, 8.1x10^20 kg, 1.6x10^21 kg)

A satellite orbits a planet at a distance r. If it has a circular orbit, the total energy (E=K+U) of the satellite is equal to:

Hint: F_centripetal=mv^2/r pick from: (E=0, E=-U/2, E=U, E=U/2)

A probe is brought to rest a distance of 1.5x10^11 m from the Sun, and allowed to fall directly into the Sun. How fast will the probe be moving when it collides with the Sun? The mass of the Sun is 2.0x10^30 kg, and its radius is 7.0x10^8 m. Hint: Consider energy conservation. pick from: (620 km/s, 42 km/s, 1.8x10^6 km/s, 3.8x10^5 km/s)

A neutron in a nuclear reactor makes an elastic, head-on collision with the nucleus of a carbon atom initially at rest.

(a) What fraction of the neutron's kinetic energy is transferred to the carbon nucleus? (The mass of the carbon nucleus is about 12.0 times the mass of the neutron.)

__________

b) The initial kinetic energy of the neutron is 2.70 10-13 J. Find its final kinetic energy and the kinetic energy of the carbon nucleus after the collision.

neutron __________J

carbon nucleus __________J

Inez is putting up decorations for her sister's quinceanera (fifteenth birthday party). She ties three light silk ribbons together to the top of a gateway and hangs from each ribbon a rubber balloon. To include the effects of the gravitational and buoyant forces on it, each balloon can be modeled as a particle of mass m=2.79 g, with its center 48.7 cm from the point of support. To show off the colors of the balloons, Inez rubs the whole surface of each balloon with her woolen scarf, to make them hang separately with gaps between them. The centers of the hanging balloons form a horizontal equilateral triangle with sides 30.2 cm long. What is the common charge each balloon carries?

A block with mass m = 17.2 kg slides down an inclined plane of slope angle 13.8^o with a constant velocity. It is then projected up the same plane with an initial speed 4.05 m/s. How far up the incline will the block move before coming to rest?

a. A child is sitting on the outer edge of a merry-go-round that is 3.19 m in diameter. If the merry-go-round makes 8.9 rev/min, what is the velocity of the child in m/s?

b. A markswoman of mass 73 kg shoots a bullet of mass 96 grams at a muzzle velocity of 696 m/s. What should the recoil speed of the markswoman be, if she is standing on a slick surface?

c. A golf ball of mass 0.050 kg has a velocity of 102 m/s immediately after being struck. If the club and ball were in contact for 0.59 ms, what is the average force exerted on the ball?

d. An undiscovered planet many light years from Earth has one moon in orbit. This moon takes 16.8 days on average to complete a nearly circular revolution around the planet. If the distance from the center of the moon to the surface of the planet is 432 x 10⁶ m and the planet has a radius of 4.14 x 10⁶ m, calculate the moon’s radial acceleration.

1. In a high temperature experiment an ozone molecule, O3, moving right at 1.5 × 103 m/s, collides head-on with an oxygen molecule, O2, which is moving to the left at 400 m/s. Both of these velocities are for the molecules viewed from the Earth frame. No chemical reaction takes place but the ozone becomes “vibrationally excited” during the interaction so that its internal energy increases by 1.4 × 10−20 J. You will need the inertias of the molecules, but you can look up the inertias of O2 and O3 molecules yourself. The collision takes place in gas phase, so the nearest other molecules are very far away compared with the size of the molecules. Molecular scale collisions like this take place in extremely short times (of order 10−15 s is fairly typical).

(a) Is the system of the O2 and O3 molecules isolated? Explain.

(b) Is the system of the O2 and O3 molecules closed? Explain.

(c) What kind of collision is this (elastic, inelastic, totally inelastic, explosive separation)? Explain.

(d) Find the center of mass velocity of the system, then transform the velocities of the molecules into the center of mass frame. (e) Find the velocity of the ozone molecule after the collision, in the Earth frame.

(f) What is the minimum relative speed of the two molecules that would allow it the ozone molecule to be excited into this vibrational state with Eint = 1.4 × 10−20 J?

Explain why the radial velocity (or gravitational tugs) method is unable to detect Earth-like planets orbiting other stars.

Hi can you please answer the question correctly please. I WILL RATE YOU. : ) We can use any source that answers the prompt.

Angular momentum: Let the Hamiltonian of our particle be described as H = ??^2 where J is the angular momentum operator. a) Diagonalise the Hamiltonian for j=0,1

b) Use explicit form of J+ and J- rising and lowering operators and Jz operator to obtain the 4 lowest energy levels for j=0,1 .

Adjacent antinodes of a standing wave on a string are 15.0 cm apart. A particle at an antinode oscillates in simple harmonic motion with amplitude 0.850 cm and period 0.0750 s. The string lies along the +x-axis and is fixed at x=0.

What is the amplitude of the two traveling waves that form this pattern?

What is the speed of the two traveling waves that form this pattern?

Find the maximum and minimum transverse speeds of a point at an antinode.

What is the shortest distance along the string between a node and an antinode?