1. If you double the length of a pendulum, how will its period change?
2. (a) What is the length of a pendulum that has a period of 0.25 s? (b) What is the period of a pendulum of length 0.25 m?
3. (a) When a wave moves through water, how do the water particles behave? (b) What is actually moving in the direction of the wave?
4. What is a common misconception about water waves?
5. What is the relationship between wave speed, frequency, and wavelength?

Charged Spheres #1 Charged spheres are placed as follows:

Determine the electric field (x and y components) created by charge A at the location (-2.0, 0.0).

Determine the electric field (x and y components) created by charge B at the location (-2.0, 0.0).

Determine the net electric field (x and y components) at the location (-2.0, 0.0).

Determine the net electric field (magnitude and direction) at the location (-2.0, 0.0).

Determine the electric force (magnitude and direction) on an electron placed at the location (-2.0, 0.0). Do not use Coulomb’s law to do so. If you do, then you will get a zero on this assignment.

An aluminum rod with a square cross section is 1.2 m long and 5.0 mm on edge. (a) What is the resistance between its ends? (b) What must be the diameter of a cylindrical copper rod of length 1.2 m if its resistance is to be the same as that of the aluminum rod? The resistivity of aluminum is 2.75 × 10-8 Ω·m and the resistivity of copper is 1.69 × 10-8 Ω·m.

Given a 2.00 μF capacitor, a 5.25 μF capacitor, and a 2.50 V battery, find the charge on each capacitor if you connect them in the following ways.

(a) in series across the battery 2.00 μF capacitor μC 5.25 μF capacitor

(b) in parallel across the battery 2.00 μF capacitor μC 5.25 μF capacitor

250 mL of water at 20.0 ∘C is placed in the freezer compartment of a refrigerator with a coefficient of performance of 4.00. How much heat energy is exhausted into the room as the water is changed to ice at -5.00 ∘C?

How do you relate the principle of Superposition to sound? Why does some people in a big room, hear quiet sound?

Describe two methods of determining the whole volume of a wooden rod

An object has a mass in air of 0.0832 kg, apparent mass in water of 0.0673 kg, and apparent mass in another liquid of 0.0718 kg. What is the specific gravity of the other liquid?

In the “old days”, televisions were made from Cathode Ray Tubes whereby a beam of
electrons rapidly swept across the inside of the screen as a result of strategic deflections
from magnetic fields acting on the beam. Suppose that Frank has a massive 2000 inch
TV in which the image has to be updated 100 times per second (to minimize the
appearance of “flicker”) and that there are 100,000 rows.
(a) Show that the electron beam moves across the screen with a speed v  c .
(b) Explain why this superluminal speed does not contradict relativity. In particular, why
can’t information be transmitted from one side of the screen to the other with v  c ?

   \(\int_{0}^{\pi}e^xsinx dx\) with n=6 subdivisions

1) Find the exact value of the integral

2) Approximate the integral using the trapezoidal rule, midpoint rule and simpson rule.

3) Find the errors using each of these rules

4) For each of these rules, show how large n should be, to be within .0001 of the actual answer.

A golfer stands 5m above the fairway and drives a golf ball with an initial velocity of v0=(0,20,49)m/s. The golferwishes to impart slice to the golf ball, which is modeled by an acceleration of 1.2m/s^2 in the x direction. Thus the acceleration function is given by: a(t)=(1.2,0,-9.8).

assuming r(0)=(0,0,5), determaine: A) the velocity and position functions.

B) the maximum height of the golf ball.

C)the range of the shot:that is, the distance between where the ball lands and (0,0,0)

A normal refrigeration cycle uses one coolant, so why does vapor compression cycle of an ice rink you a primary coolant and a secondary coolant?

A block with mass m1 = 8.7 kg is on an incline with an angle θ = 38° with respect to the horizontal. For the first question there is no friction, but for the rest of this problem the coefficients of friction are: μk = 0.34 and μs = 0.374.

1) When there is no friction, what is the magnitude of the acceleration of the block?

2) Now with friction, what is the magnitude of the acceleration of the block after it begins to slide down the plane?

3) To keep the mass from accelerating, a spring is attached. What is the minimum spring constant of the spring to keep the block from sliding if it extends x = 0.16 m from its unstretched length.

4) Now a new block with mass m₂ = 14.8 kg is attached to the first block. The new block is made of a different material and has a greater coefficient of static friction. What minimum value for the coefficient of static friction is needed between the new block and the plane to keep the system from accelerating?

A mass oscillates on a spring with a period T and an amplitude 0.48 cm. The mass is at the equilibrium position x=0 at t=0, and is moving in the positive direction.

a.) Where is the mass at the time t=T/8?

b.) Where is the mass at the time t=T/4?

c.) Where is the mass at the time t=T/2?

d.) Where is the mass at the time t=3T/4?

e.) Plot the position versus time graph with the vertical axis representing position and the horizontal axis representing time for 0≤t≤T. Give the values with the step of Δt=T/8.