A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis.

Part A)

What is the electric potential at the point on the x-axis where the electric field is zero? Answer in V

Part B)

What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero? Answer in N/C

An object with total mass m_total = 14.6 kg is sitting at rest when it explodes into three pieces. One piece with mass m₁ = 4.7 kg moves up and to the left at an angle of θ₁ = 20° above the –x axis with a speed of v₁ = 26.8 m/s. A second piece with mass m₂ = 5.1 kg moves down and to the right an angle of θ₂ = 25° to the right of the -y axis at a speed of v₂ = 23.5 m/s.

What is the x-component of the velocity of the third piece?

What is the y-component of the velocity of the third piece?

What is the magnitude of the velocity of the center of mass of the pieces after the collision?

Calculate the increase in kinetic energy of the pieces during the explosion.

1. Derive PV^Gamma = constant

2. All adiabatic relations

An 8000 kg truck traveling with a velocity of 20. 0 m/s in a direction 30 ° south of east and a 6250 kg car traveling with a velocity of 25. 0 m/s 40 ° north of east collide in a perfectly inelastic collision. Find (a) the final speed and (b) the direction of the combined mass. Also, calculate (c) the change in the kinetic energy of the system.

1. Determine the variance in position and momentum, Δx²=<x²>−<x>² and Δp²=<p²>−<p>² for the ground-state SHO and show that they satisfy the Heisenberg uncertainty relation, (Δx)(Δp)≥ℏ2

Two cars are approaching each other, one traveling north with a momentum of 3 kg-m/s and one traveling east with a momentum of 4 kg-m/s. The two cars collide and stick together. Right after the collision (choose all that apply)

1. the eastern component of the momentum of the two cars is 4 kg-m/s.

2. the northern component of the momentum of the two cars is 3 kg-m/s.

3. the total momentum of the two cars is 7 kg-m/s

A symmetrical table of height 0.750 m, length 1.55 m, and weight 462 N is dragged across the floor by a force applied to its front edge. The force is directed to the right and upward and makes an angle of 30.0° with the horizontal.

(a) Find the minimum force necessary to drag the table across the floor. The coefficient of sliding friction between table and floor is 0.375. 164.45 N
  

(b) Calculate the normal force and the frictional force on each leg.

The formula for length contraction gives the length of an interval on a ruler moving with velocity v relative to an observer as where L is the length of the same interval on a ruler at rest with respect to the observer. By what fraction is the length of a meter stick reduced if its velocity relative to you is measured to be 87 percent of the speed of light?

Sound with a frequency 710 Hz from a distant source passes through a doorway 1.17 m wide in a sound-absorbing wall.

(a) Find the number of the diffraction minima at listening positions along a line parallel to the wall.


(b) Find the angular directions of the diffraction minima at listening positions along a line parallel to the wall. (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.)

A 10 g bullet traveling at 350 m/s strikes a 9.0 kg , 1.2-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door just after impact?

The wạlls of ạn ice chest ạre mạde of 2.00-mm-thick insulạtion hạving ạ thermạl conductivity 0.00300 W/m∙K. The totạl surfạce ạreạ of the ice chest is 1.20 m². The temperạture of the outside surfạce of the chest is 20.0 °C. The lạtent heạt of fusion of wạter is 334 kJ/kg.

How mạny hours (time) does it tạke to melt 4.00 kg of ice plạced inside the ice chest?

A solid, uniform disk of radius 0.250 m and mass 60.6 kg rolls down a ramp of length 4.80 m that makes an angle of 12.0° with the horizontal. The disk starts from rest from the top of the ramp.

(a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp.
m/s

(b) Find the angular speed of the disk at the bottom of the ramp.
rad/s

A nonconducting ring of radius of 11.6 cm is uniformly charged with a total positive charge of 10.0 µC. The ring rotates at a constant angular speed 18.6 rad/s about an axis through its center, perpendicular to the plane of the ring. What is the magnitude of the magnetic field on the axis of the ring 5.00 cm from its center?
pT

A charge of 2.20 µC is uniformly distributed on a ring of radius 9.0 cm. Find the electric field strength on the axis at the following locations. (be careful calculating c and d the last post was wrong. please include e.)

(a) 1.2 cm from the center of the ring
  N/C

(b) 3.9 cm from the center of the ring
  N/C

(c) 4.0 m from the center of the ring
  N/C

(d) Find the field strength at 4.0 m using the approximation that the ring is a point charge at the origin.
  N/C

(e) Compare your results for parts (c) and (d) by finding the ratio of the approximation to the exact result.


(f) Is your approximation result a good one? Explain your answer. (Do this on paper. Your instructor may ask you to turn in your work.)