A standard flashlight battery can deliver about 4.9 W·h of energy before it runs down. (a) If a battery costs 80 cents, what is the cost in dollars of operating a 100 W lamp for 11 h using batteries? (b) What is the cost in dollars if power is provided at the rate of 6.0 cents per kilowatt-hour?

Suppose you throw a ball into the air. Do you think it takes longer to reach its maximum height or to fall back to earth from its maximum height? We will solve the problem in this project, but before getting started, think about that situation and make a guess based on your physical intuition. 1. A ball with mass m is projected vertically upward from the earth’s surface with a positive initial velocity v0. We assume the forces acting on the ball are the force of gravity and a retarding force of air resistance with direction opposite to the direction of motion and with magnitude p|v(t)|, where p is a positive constant and v(t) is the velocity of the ball at time t. In both the ascent and the descent, the total force acting on the ball is pv mg. (During ascent, v(t) is positive and the resistance acts downward; during descent, v(t) is negative and the resistance acts upward.) So, by Newton’s Second Law, the equation of motion is mv0 = pv mg Solve this di↵erential equation to show that the velocity is v(t) = ✓ v0 + mg p ◆ ept/m mg p 2. Show that the height of the ball, until it hits the ground, is y(t) = ✓ v0 + mg p ◆ m p ⇣ 1 ept/m⌘ mgt p 3. Let t1 be the time that the ball takes to reach its maximum height. Show that t1 = m p ln ✓mg + pv0 mg ◆ Find this time for a ball with mass 1 kg and initial velocity 20 m/s. Assume the air resistance is 1 10 of the speed. 1 4. Let t2 be the time at which the ball falls back to earth. For the particular ball in Problem 3, estimate t2 by using a graph of the height function y(t). Which is faster, going up or coming down? 5. In general, it’s not east to find t2 because it’s impossible to solve the equation y(t)=0 explicitly. We can, however, use an indirect method to determine whether ascent or descent is faster: We determine whether y(2t1) is positive or negative. Show that y(2t1) = m2g p2 ✓ x 1 x 2 ln x ◆ where x = ept1/m. Then show that x > 1 and the function f(x) = x 1 x 2 ln x is increasing for x > 1. Use this result to decide whether y(2t1) is positive or negative. What can you conclude? Is ascent or descent faster?

Please answer #3

Please restate the problem to be solved, and define all variables and parameters. Please explain your reasoning and strategy for solving the problem. Please go over basic principals or key processes underlying the problem that was addressed in the paper. Please include an interpretation of the information in the context in which the problem was solved. Please state your conclusions in complete sentences which stand on their own

Sorry, I know this is a lot

A thin, cylindrical rod ℓ = 27.0 cm long with a mass m = 1.20 kg has a ball of diameter d = 10.00 cm and mass M = 2.00 kg attached to one end. The arrangement is originally vertical and stationary, with the ball at the top as shown in the figure below. The combination is free to pivot about the bottom end of the rod after being given a slight nudge.

I am looking for the; How does it compare with the speed had the ball fallen freely through the same distance of 32.0 cm?

As well as the V swing and the V fall. (There is the exact question of this on chegg already posted if needing to see the other parts of the question in order to get this answer)

An object of mass 0.50 kg is released from the top of a building of height 2 m. The object experiences a horizontal constant force of 1.1 N due to a wind blowing parallel to the face of the building.

(a) Find the time it takes for the object to strike the ground. _____s

(b) What is the magnitude of the acceleration of the object? ______m/s2

(c) Through what horizontal distance does the object move before it hits the ground? _____m

A string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle. The pulley is initially not turning. A constant force of 50 N is applied to the string, which does not slip, causing the pulley to rotate and the string to unwind. If the string unwinds 1.2 m in 4.9 s, what is the moment of inertia of the pulley?

Radiation force balance power meters are commonly used
to measure output acoustic power of ultrasound transducers.
Two types of targets are usually used in these devices:
a flat perfect absorber, or a cone-shape perfect reflector.
What would be the angle theta for a cone perfect reflector in order to
get identical power readings for a given ultrasound exposure
with two different type of targets? Assume that the two targets have
equal surface areas.

You must provide a proof for your answer

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.