For the following parts, assume you have a hollowed solid where the hollow region has a radius of 1/3 of the whole solid and the charge density can be expressed as

?=??² with units of ?/?³

where r is measured in meters and β is a constant. Determine the value and units of β for the following cases: a) a sphere with outer radius of 12.0 cm and total charge of +8.73 μC and b) a cylinder with an outer radius of 15.0 cm, length of 50.0 cm, and total charge of – 6.73 μC. [Answers: 0.140, 0.017]

A block of 4 kg moves in the +x direction with a velocity of 15 m/s while a block of 6 kg moves in the +y direction with a velocity of 10 m/s. They collide and stick together.

Calculate the following: a. What is the momentum in this system? b. What is the final velocity of the two blocks?

6. A cannon ball is fired from a giant cannon whose length is 1.00 x 10² m. The cannon ball leaves the barrel at a speed of 99.5 m/s:

a. What is the acceleration of the cannon ball while in the cannon? Show all work.

The cannon ball (above) leaves the barrel at ground level at an angle of 60.0^o from the ground and travels with minimal air resistance until impacting on the ground some distance away.

b. Calculate the initial vertical and horizontal components of the cannon ball’s velocity.

c. (1) Calculate the time needed to reach maximum height. (2) Calculate time in flight.

d. Calculate the range of the cannon.

e. Calculate the maximum height that the cannon ball reaches.

a) Assume that there is a long ideal solenoid with 120 turns/cm. It carries a current i= 2 A and it has a diameter 2 cm and a length 5 m. Find the uniform magnetic field inside the solenoid.

c) Now, construct an RL circuit using an ideal battery that has potential difference 5 V, one resistor with R = 2 Ω and the solenoid that has same shape with one mentioned at part (a). Wait very long time and then remove the battery. Find the potential difference across resistor at 2 ms after removing battery? (Hint: First calculate the inductance)

How do we implement new technology within the respiratory field without bringing harm to the patient?

For both resistances, plot the charge curve of ln(1-V/V0) vs. time. From the slope of the line, calculate the C (capacity). Please demonstrate in detail how to figure out some of the points of ln(1-V/V0), how to determine the slope of the graph, and how to plot graph in Excel if possible. Thank you.

A roller coaster car with a mass 700 Kilograms starts from rest at h₁ above the ground and slides along a track. The car encounters a loop of radius 12 m. The bottom of the loop is a height h₂ = 5 m from the ground. What would be the max height of release h₁ for the roller coaster car if the amount of thermal energy produced between the point of release and the top of the loop should not exceed 15% of the initial mechanical energy and the normal force at the top should be no more than 580 N? answer in meters

1 (a) . Show that the zero-point energy of a Debye solid composed of N atoms is equal to 9/8NkΘD. This implies, for each vibrational mode of the solid, a mean zero-point energy 3/8 kΘD, that is,  = 3/4 ωD.

(b)Show that, for T < θd,="" the="" quantity="">P − CV) of a Debye solid varies as T7 and hence the ratio (CP/CV)  1

What is the correct line of thinking in dealing with a statics problem where one must determine the resultant force from multiple vectors using a unit triangle instead of cos and sin; ie. how do you use a unit triangle?

Two bicycle tires are set rolling with the same initial speed of 3.70 m/s along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes a distance of 17.8 m ; the other is at 105 psi and goes a distance of 93.3 m . Assume that the net horizontal force is due to rolling friction only and take the free-fall acceleration to be g = 9.80 m/s2 .

a)What is the coefficient of rolling friction μr for the tire under low pressure?

A bullet of mass m=14 gr is fired into a block of mass M=1 kg initially at rest at the edge of a frictionless table of height h=1.10 m. The bullet remains in the block and the block lands a distance d=0.65 m from the bottom of the table.

Determine the initial velocity of the bullet.

Determine the loss of kinetic Energy during the collision

A bullet of mass m=12 gr is fired into a block of mass M=1 kg initially at rest at the edge of a frictionless table of height h=1.00 m. The bullet remains in the block and the block lands a distance d=0.60 m from the bottom of the table. a)Determine the initial velocity of the bullet. vi= m/s b) Determine the loss of kinetic energy during the collision. ΔK = J

A proton is traveling horizontally to the right at 4.00×106 m/s. (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of 1.67 cm. (b) How 7 much time does it take the proton to stop after entering the field?A −1.00-nC point charge is at the origin, and a +4.00-nC point charge is on the y-axis at y = 2.00 m. (a) Find the electric field (magnitude and direction) at each of the following points on the y-axis: (i) y = 3.00 m; (ii) y = 1.00 m; (iii) y = −2.00 m. (b) Find the net electric force that the two charges would exert on an electron placed at each point in part (a).