Write down a summary statement relating position and velocity in your own words, in graphical form, and in mathematical form.

A 3 kg pendulum bob on a 2 m long string is released with a velocity of 2 m/s when the support string makes an angle of 44 degrees with the vertical.  Calculate the tension in the string at the highest position of the bob.

A plate capacitor C has an initial charge Q and plates separation d. A dielectric material (k=2) is inserted between the plates at the mean while the separation parallel between the plates is doubled (to become 2d). So, in this process one statement below is wrong:

a) U is the same

b) Q is the same

c) V is the same

d) E is the same

Give an example of the Continuity Equation, Bernoulli's equation and the Poiseuille Principle

a 70 kg skier is being towed on a rope behind a 450 kg snowmobile on a smooth, snow covered surface at 14 m/s when the snowmobile hits a patch of muddy ground that brings it to a hlat in 10m

What is the average acceleration of the center of mass of the skier-snowmobile system?

When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 72.9-kg man just before contact with the ground has a speed of 8.74 m/s. (a) In a stiff-legged landing he comes to a halt in 1.71 ms. Find the magnitude of the average net force that acts on him during this time. (b) When he bends his knees, he comes to a halt in 0.268 s. Find the magnitude of the average net force now. (c) During the landing, the force of the ground on the man points upward, while the force due to gravity points downward. The average net force acting on the man includes both of these forces. Taking into account the directions of the forces, find the magnitude of the force applied by the ground on the man in part (b).

An ideal gas with γ=1.4 occupies 4.5 L at 300 K and 110 kPa pressure and is compressed adiabatically until its volume is 2.0 L. It's then cooled at constant pressure until it reaches 300 K, then allowed to expand isothermally back to stateA.

Find the net work done on the gas.

Find the minimum volume reached.

A circular loop in the plane of a paper lies in a 0.45 T magnetic field pointing into the paper. The loop's diameter changes from 23.0 cm to 6.8 cmin 0.54 s .

What is the magnitude of the average induced emf?

What is the average induced current if the coil resistance is 3.9 Ω ?

What is the energy needed to cause an electron to undergo a transition from the n = 4 state to the n = 5 state in hydrogen?

1. Investigate the difference between "phase velocity" and "group velocity." Why does an index of refraction of less than 1 (so v>c) not violate relativity, which says no information can move faster than the speed of light?

6. A 200-kg roller coaster reaches the top of the steepest hill with a speed of 5.80 km/h. It then descends the hill, which is at an angle of 35° and is 41.0 m long. What will its kinetic energy be when it reaches the bottom? Assume µk = 0.18.

a piece of solid lead weighing 6.5 kg at 327 degrees celsius receives 150000 joules of heat.. in what state is the lead after this occurs? the latent heat of fusion for lead is 23200 J/kg

Which of the statements regarding this situation are true? Select all that apply.

• -For a conducting sphere with a net charge Q, the electric field inside the sphere is zero and the electric field outside the sphere is the same as the field from a point charge of charge Q placed at the center of the sphere.
  

• -When one charged sphere is placed inside another the net electric field outside the larger sphere is always larger than the field due to the larger sphere alone.
  

• -When one charged sphere is placed inside another the net electric field outside the larger sphere is always non-zero.
  

• -As you move steadily out from the origin in this simulation the electric field changes smoothly. The field can never jump suddenly from one value to another.
  

• -If the outer sphere is present the electric field between its inner radius and its outer radius (inside its solid wall, in other words) is always zero.
  

• -If the outer sphere is present the way charge is distributed on the outer sphere depends only on its charge, and not on the charge of the point charge and the inner sphere.
  

• -It is possible to have no electric field inside the outer sphere and a non-zero electric field outside the outer sphere.
  

• -It is not possible to have a non-zero electric field inside the inner sphere and outside the outer sphere, but no electric field between the inner and outer spheres.
  

• -If there is a positive point charge present at the center, the field in all regions is either zero or directed away from the center.

Two ice skaters, Daniel (mass 65.0kg ) and Rebecca (mass 45.0kg ), are practicing. Daniel stops to tie his shoelace and, while at rest, is struck by Rebecca, who is moving at 13.0m/s before she collides with him. After the collision, Rebecca has a velocity of magnitude 8.00m/s at an angle of 53.1? from her initial direction. Both skaters move on the frictionless, horizontal surface of the rink.

Part A

What is the magnitude of Daniel's velocity after the collision?

Part B

What is the direction of Daniel's velocity after the collision?

Part C

What is the change in total kinetic energy of the two skaters as a result of the collision?

A cyclist turns her bicycle upside down to repair it. She then notices that the front wheel is executing a slow, small amplitude, back-and-forth rotational motion with period 12 s. Treating the wheel as a thin ring of mass 600 g and radius 30 cm, whose only irregularity is the tire valve stem, determine the mass of the valve stem.