A point charge with a mass of 1.81 ng and a charge of +1.22 ?C moves in the x-y plane with a velocity of 3.00 x 104 m/s in a direction 15° above the +x-axis. At time t=0, the point charge enters a uniform magnetic field of strength 1.25 T that points in the +x-direction.Assume that the point charge remains immersed in the uniform magnetic field after time t=0.

a) What is the magnitude and direction of the magnetic force that the magnetic field exerts on the point charge at time t=0?

b) How does the x-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

c) How does the y-component of the charge’s initial velocity effect the motion of this point charge as it moves through the uniform magnetic field? Does its magnitude change? Does its direction change? Explain your reasoning.

d) Use your answers from parts 1b & 1c to explain why the path of this point charge is helical (corkscrew-shaped). Explain your reasoning.

e) Determine the radius of the circular part of the point charge’s helical path.

A torque of 36.2 N · m is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from 0 to 9.5 rad/s. After 6.10 s the directed force is removed, and the wheel comes to rest 60.2 s later.

A- What is the wheel's moment of inertia

B- What is the magnitude of the torque caused by friction

C- From the time the directed force is initially applied, how many revolutions does the wheel go through?

A cart of mass m1 = 5.69 kg and initial speed = 3.17 m/s collides head-on with a second cart of mass m2 = 3.76 kg, initially at rest. Assuming that the collision is perfectly elastic, find the speed of cart m2 after the collision.

A bullet flies horizontally, hits a wooden block suspended from a 1.0 m string, and gets stuck in the block. The angle of deviation of the string equals 11 degrees. The mass of the bullet is 1000 times smaller than the mass of the block. What is the initial speed of the bullet? Point out the laws of physics in the solution and show all steps.

A 5.1 cm diameter horizontal pipe gradually narrows to 2.5 cm . When water flows through this pipe at a certain rate, the gauge pressure in these two sections is 35.0 kPa and 21.8 kPa , respectively. What is the volume rate of flow?

A transverse wave propagates in a very long wire of mass per unit length 4 x 10^3 kg/m and under tension of 360 N. An observer next to the wire notices 10 wave peaks (or 'crests') passing her in a time of 2 seconds moving to the left.

a. If at t = 0 and x = 0 the displacement assumes its maximum value of 1 mm, what is the explicit equation for the wave?

b. Calculate the maximum longitudinal velocity for a infinitesimal segment of the wire (a 'particle' on the wire if you like)?

Now assume the same wire has been fixed on both ends so that the two fixed points are separated by unknown length L. The tension remains the same. One of the resonance frequencies of the wire is 375 Hz. The next higher resonance frequency is 450 Hz.

c. What is the fundamental frequency of the string?

1. Engineers are designing a rocket to be used in deep space. If the rocket is fired from rest in deep space, the total mass of the rocket, payload, and unspent fuel must reach a speed of 1.10 ✕ 10⁴ m/s in order to accomplish other maneuvers. Due to the amount of fuel which is still onboard, the rocket, payload, and unspent fuel will have a final mass of 4.10 ✕ 10³ kg. If the design of the rocket is such that the exhaust speed is 2.55 ✕ 10³ m/s, determine the amount of fuel required to perform this maneuver.

2. A 51.0 kg astronaut has been spacewalking outside her spacecraft and realizes that she is stranded (stationary) a distance of d = 15.0 m from the outside of the spacecraft. In order to get back, she throws a 1.25 kg hammer directly away from the ship. If the spacecraft is a sphere with a 2.00 m radius, determine the distance of the hammer from the outside of the ship when she reaches the safety of the ship.

3. An ice skater with a mass of 51.0 kg is gliding across a smooth lake with a speed of 2.05 m/s when she hits a spot of ice covered with snow. After a time of 7.65 s she has slowed to a stop. Using your knowledge of momentum, determine the magnitude of the average force of friction acting on the ice skater while she slows to a stop.

You are pushing a sled in which your little sister is seated up a 26° slope (one that makes an angle of 26° with the horizontal). If the mass of the sled and girl is 46 kg, and the coefficient of kinetic friction between the sled and the surface is 0.100, with what force (in N) do you need to push in order for the sled to move with constant velocity?

Will a copper wire or an aluminum wire give the larger current to weight ratio for high voltage transmission lines if both wires are to have the same resistance between any two points?

A parallel-plate capacitor is made from two aluminum foil sheets, each 5.4 cm long and 4.9 cm wide. The two sheets are separated by a distance of 0.024 mm.

1)

What is the capacitance of this capacitor?

C =   μF   

2)

If a potential difference of 2 volts is applied across the two plates of this capacitor, what is the absolute value of the charge on the plate with the higher voltage?

q_higher =   μC  

3)

What is the absolute value of the charge on the plate with the lower voltage?

q_lower =   μC  

4)

Now a piece of teflon with a dielectric constant of κ = 2.1 is inserted to fill the space between the plate.

What is the capacitance of the capacitor with the teflon inserted?

C =    μF  

5)

If a potential difference of 2 volts is applied as before across the two plates of this capacitor, what is the absolute value of the charge on the plate with the higher voltage with the teflon inserted?

q_higher =    μC  

6)

Based on your above calculations, did the capacitance of the capacitor increase or decrease when the teflon was inserted?

• (1) increase
• (2) stayed the same
• (3) decrease

7)

Based on your above calculations, did the amount of charge on the plate with the higher voltage increase or decrease when the teflon was inserted?

• (1) increase
• (2) stayed the same
• (3) decrease

8) What is the distance to a particular star system measured by an observer in a rocket ship traveling to the star system with a speed of 0.95c? (The distance is 37 trillion km as measured by an observer on Earth.)
____ km

9) A spacecraft has a velocity of 20 m/s and an acceleration of 40 m/s² and is descending to land on planet Y and slows down by 4 m/s every second. The strength of the planet's gravitational field is 7 N/kg. If the passengers in the spacecraft account for the forces they feel in terms of a single gravitational field, how strong would this field have to be?
____ N/kg

explain in physics how the eye works and explain physics causing common vision defects and explain the physics of how they are corrected

As part of an experiment in physics lab, small metal ball of radius r = 2.3 cm rolls without slipping down a ramp and around a loop-the-loop of radius R = 3.4 m. The ball is solid with a uniform density and a mass M = 373 g.

How high above the top of the loop must it be released in order that the ball just makes it around the loop?

Now instead of a sphere, what if we rolled a solid disk with the same mass and radius. How high above the top of the loop must it be released in order that the disk just makes it around the loop?

Finally, what if we had allowed a block with the same mass as the sphere to slide on the ramp. The block slips without friction but does not rotate. How high above the top of the loop must it be released in order that the block just makes it around the loop?