A mortar* crew is positioned near the top of a steep hill. Enemy forces are charging up the hill and it is necessary for the crew to spring into action. Angling the mortar at an angle of θ = 57.0o (as shown), the crew fires the shell at a muzzle velocity of 241 feet per second. How far down the hill does the shell strike if the hill subtends an angle φ = 36.0o from the horizontal? (Ignore air friction.)

How long will the mortar shell remain in the air?

How fast will the shell be traveling when it hits the ground?

An extremely small sample of an ideal diatomic gas (with a molar mass of 28 g/mol) has the following distribution of molecular speeds: 1 molecule moving at 100 m/s, 2 molecules at 200 m/s, 4 at 300 m/s, and 3 at 400 m/s.

What is the rms speed of the distribution? What is the average kinetic energy of translational motion per molecule? What is the temperature of this sample?

An insulated Thermos contains 145 g of water at 70.7 ˚C. You put in a 11.0 g ice cube at 0.00 ˚C to form a system of ice + original water. The specific heat of liquid water is 4190 J/kg•K; and the heat of fusion of water is 333 kJ/kg. What is the net entropy change of the system from then until the system reaches the final (equilibrium) temperature?

Small charged spheres are arranged as follows:

1. Determine the signs of the charged spheres. Explain.

2. Determine the net electric field (magnitude and direction) at the origin.

3. Using your result from part b, determine the net electric force (magnitude and direction) on a proton initially placed at rest at the origin. If you don't use your result from part b, then you will not get any credit whatsoever on this part.

4. Determine the acceleration (magnitude and direction) of the proton (you may ignore gravity).

5. Could you use the constant-acceleration kinematics equations to predict the subsequent motion of the proton? Explain.

69) A particle with a mass of 400 g movig at 2.0 m/s collides elastically with a stationary particle whose mass is 240 g.

After the collision, the 400 g mass is moving at 1.5 m/s. Through what angle is its path deflected?

The answer is 30. Please show all the work with fomular.

A small solid sphere of mass M₀, of radius R₀, and of uniform density ?₀ is placed in a large bowl containing water. It floats and the level of the water in the dish is L. Given the information below, determine the possible effects on the water level L, (R-Rises, F-Falls, U-Unchanged), when that sphere is replaced by a new solid sphere of uniform density.
Read it to me

R F U R or U F or U R or F or U  The new sphere has radius R = R₀ and density ? < ?₀
R F U R or U F or U R or F or U  The new sphere has density ? = ?₀ and mass M < M₀
R F U R or U F or U R or F or U  The new sphere has density ? > ?₀ and mass M = M₀
R F U R or U F or U R or F or U  The new sphere has radius R > R₀ and density ? < ?₀
R F U R or U F or U R or F or U  The new sphere has mass M > M₀ and density ? = ?₀
R F U R or U F or U R or F or U  The new sphere has density ? < ?₀ and mass M = M₀

Problem 22.29

What magnitude charge creates a 1.70 N/C electric field at a point 4.60 m away? Express your answer with the appropriate units. Thanks ;)

Which one of the following statements is true? Please explain each choice: why it is true/false.

(a) The Burgers vector of an edge dislocation is normal to the dislocation line and normal to the slip plane.

(b) The Burgers vector of a screw dislocation is normal to the dislocation line and parallel to the slip plane.

(c) When a screw dislocation enables slip in a single crystal, the dislocation line remains in the slip plane.

(d) BCC crystals do not contain dislocations.

(e) Fine-grained samples of γ-iron contain fewer dislocations than coarse-grained samples of γ-iron.

In the double-slit experiment of the figure below, the viewing screen is at distance D = 4.00 m, point P lies at distance y = 13.0 cm from the center of the pattern, the slit separation d is 4.50

1) Explain the working of a lightning rod. Don

8. Determine the desired quantity in each of the following collisions: (a) A student of mass 60kg sits on a rolling chair (assume no friction with the ground). He pulls out a fire extinguisher and fires 2kg of material at a velocity of 8m/s. How fast is he moving after this process? (b) A 90kg astronaut is traveling through space at a rate of 2m/s. He is holding a 5kg mass as he travels. How fast would he have to throw this mass in order to come to rest? (c) A box of mass 20kg slides across an icy floor at a rate of 5m/s. In order to stop it, we slide smaller boxes of mass of 0.8kg towards it at a rate of 1m/s. How many boxes must collide with (and stick to) it before it comes to a stop? (d) A football player with mass 70kg runs towards another at a rate of 4m/s. Realizing he’s about to get walloped, the second player runs towards the first at a rate of 2m/s. If the second player has a mass of only 50kg, what is the velocity of the pair after the collision? (e) Three billiard balls travel along a table. The first is moving rightwards with a speed of 2m/s, the second is moving leftwards with a speed of 2m/s, and the middle one lies halfway between the first two. What is the velocity of the ball in the middle after the collision?

(f) Alice, with a mass of 60kg, jumps upwards off the Earth. At the moment of her jump, how fast does she move the Earth in the opposite direction? (The mass of the earth is about 5.972 · 1024kg)

The power supplied by a torque, ?, to rotate an object at angular frequency, ?, is P = ??. A common car engine produces ? = 3000Nm at ? = 3000 RPM (rotations per minute). Suppose you want to create an electric car that runs on a battery and electric motor. Typically, electric car motors utilize a current of 100A and have a cross sectional area of 0.5m². Suppose also that the number of wire turns in the coil of the motor is N = 100.

Q1: How strong of a magnetic field is required to produce the same torque as a regular car engine?

When the motor is connected in series with the battery that powers it, we can treat it like a generic circuit element with effective resistance R that causes a voltage drop V = IR. By setting the electrical power consumed by the motor equal to the mechanical power used to push the car, P = ??, the effective resistance of the motor can be determined.

Q2: What is the effective resistance of the motor?

Q3: Determine the voltage of the battery?

Please show all work, I will rate high.

Why does a frisbee behave differently when thrown upside down?

A textbook of mass 2.00kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.100m , to a hanging book with mass 2.98kg . The system is released from rest, and the books are observed to move a distance 1.15m over a time interval of 0.850s