A block is projected up a frictionless inclined plane with initial speed v₀ = 3.48 m/s. The angle of incline is θ = 32.7°.

(a) How far up the plane does the block go?
___m

(b) How long does it take to get there?
___ s

(c) What is its speed when it gets back to the bottom?
___ m/s

Charge Q is uniformly distributed along a thin, flexible rod. The rod is then bent into a semicircle of radius R.

Find an expression for the electric potential at the center of the semicircle.

A proton with rest mass (.998GeV/c2) is moving with total energy E = 3GeV . What are its momentum

and its speed?

1. Ryan is readying for a face-off at the begninning of a hockey game. What is the total Force that ryan exerts on the ice? What is the total force of the ice on Ryan? Assume that Ryans total mass is 100 kg. Also take up ot be the +y direction, and towards the opponents goal to be +x direction.

2. Ryan is skating down the ice at 5 m/s. What is Ryan's momentum? Kinetic Energy?

3. Preparing to take a shot at the net, Ryan comes to a stop on the ice. If it takes ryan .5 seconds to come to stop, what is the net force that the ice exerts on Ryan? Use the net force to find the distance it takes ryan to come to a stop. What is the net force that Ryan exerts on the ice while stopping: give a name to this force.

4. Ryan takes a shot, sending the .2 kg puck towards the goal at 30 m/s. Assuming the collisions with the net are perfectly inelastic, and the collisions with the goalies stick are perfectly elastic, and that the goalie and net both remain at rest after the collision calculate:

a. The change in kinetic energy and momentum if the goalie blocks the puck with his stick

b. The change in KE and momentum if the puck goes into the net and stops.

A 105‑turn circular coil of radius 2.41 cm and negligible resistance is immersed in a uniform magnetic field that is perpendicular to the plane of the coil. The coil is connected to a 14.7 Ω resistor to create a closed circuit. During a time interval of 0.167 s, the magnetic field strength decreases uniformly from 0.481 T to zero. Find the energy, in millijoules, that is dissipated in the resistor during this time interval.

Answer all parts. Write big, clear and legibly.  

A 0.10kg dart is fired horizontally at the center of a 0.80kg vertically hanging block, sticking to it. The system reaches a maximum height, h, of 0.20m above the collision point.

Find:

a) the velocity of the dart – block system just after the collision

b) the velocity of the dart before collision

c) the energy lost during the collision.

d) if the dart gains its speed due to a spring system that is initially compressed 0.05m from its equilibrium

position, determine the spring constant.

e) If the dart didn’t stick to

the block, but instead fell vertically after collision, would the initial velocity of the

dart have to be greater, less than, or equal to the velocity that was found in part (b)? Justify.

An object is placed 18 cm in front of a converging lens that has a 12 cm focal length. Use ray tracing to determine the magnification of the image.

A stiff wire 44.5 cm long is bent at a right angle in the middle. One section lies along the z axis and the other is along the line y=2x in the xy plane. A current of 24.0 A flows in the wire-down the z axis and out the line in the xy plane. The wire passes through a uniform magnetic field given by B =(0.318i)T.

A) Determine the magnitude and direction of the total force on the wire. (The direction must be theta below the negative y-axis).

You and your crew must dock your 2.55 × 10⁴ kg spaceship at Spaceport Alpha, which is orbiting Mars. In the process, Alpha’s control tower has requested that you ram another vessel, a freight ship of mass 1.60 × 10⁴ kg, latch onto it, and use your combined momentum to bring it into dock. The freight ship is not moving with respect to the colossal Spaceport Alpha, which has a mass of 1.80 × 10⁷ kg. Alpha’s automated system that guides incoming spacecraft into dock requires that the incoming speed is less than 2.0 m/s.

(a) Assuming a perfectly linear alignment of your ship’s velocity vector with the freight ship (which is stationary with respect to Alpha) and Alpha’s docking port, what must be your ship’s speed (before colliding with the freight ship) in order that the combination of the freight ship and your ship arrive at Alpha’s docking port with a speed of 1.40 m/s?
(b) What will be the velocity of Spaceport Alpha when the combination of your vessel and the freight ship successfully docks with it?
(c) Suppose you made a mistake while maneuvering your vessel in an attempt to ram the freight ship and, rather than latching on to it and making a perfectly inelastic collision, you strike it and knock it in the direction of the spaceport with a perfectly elastic collision. What is the speed of freight ship in that case (assuming your ship had the same initial velocity as you had calculated in part (a))?

A solenoid of radius 3.5 cm has 800 turns and a length of 25 cm.

(a) Find its inductance.
mH

(b) Find the rate at which current must change through it to produce an emf of 90 mV. (Enter the magnitude.)
A/s

Two long thin parallel wires 13.0 cm apart carry 25-A currents in the same direction.

Part A

Determine the magnitude of the magnetic field vector at a point 10.0 cm from one wire and 6.0 cm from the other (Figure 1) .

Express your answer using two significant figures. B=?

Part B

Determine the direction of the magnetic field vector at that point.

Express your answer using two significant figures.

A particular make of light bulb contains argon at 50 Torr and has a tungsten filament of radius 0.10mm and length 5.0cm. When operating, the gas close to the filament has a temperature of about 1000°C. How many collisions are made with the filament in each second.