Problem 10: Water is drawn from a well using a leaky bucket. Assume the following: • The well is 23 ft deep and requires 23 ft of rope to pull the bucket to the top. • The rope weighs a total of 12 lbs. • The bucket weighs 3 lbs when empty. • The bucket holds 16 lbs of water. It is full at the bottom of the well and loses half of its water by the time it reaches the top of the well. • The water leaks from the bucket at a constant rate. Set up an integral expression for how much work was done when pulling the bucket up the first 7 ft on its way to the top.

How are the arrangement of and movement of the particles that make up a gas different than the arrangement and movement of the particles that make up solid to liquids?

A 0.5530-kg ice cube at -12.40°C is placed inside a chamber of steam at 365.0°C. Later, you notice that the ice cube has completely melted into a puddle of water. If the chamber initially contained 6.310 moles of steam (water) molecules before the ice is added, calculate the final temperature of the puddle once it settled to equilibrium. (Assume the chamber walls are sufficiently flexible to allow the system to remain isobaric and consider thermal losses/gains from the chamber walls as negligible.)

A.) Find the work done by an ideal engine which extracts 8900.0 J of heat from its hot resevior while operating between 550.0 K and 370.0 K.

B.) The work from the engine goes into an ideal refridgerator which extracts 5300.0 J of heat from its cold resevior. FInd the coefficient of performance of the ideal refridgerator.

A projectile is shot from the edge of a cliff at an initial speed of 5.0 m/s at angle 30o with the horizontal. After 12 seconds, the projectile hits the ground below at some point P. (a) Determine the height of the cliff above ground level. (b) Determine the distance of the point P from the base of the vertical cliff. (c) At the instant just before the projectile hits point P, find the horizontal and the vertical components of its velocity

Please show the work for how to get the answer. Thank you in advance.

Assume that all of the mass of a bicycle wheel is concentrated at its rim. Such a wheel of mass 1.2 kg and radius 30 cm starts from rest at the top of a hill 100 m long and inclined at 20� to the horizontal. What will be the speed of the wheel at the bottom of the hill if it rolls without slipping?
(Answer: 15 m/s)

A long straight wire lies on a horizontal table and carries an ever-increasing current toward the north. Two coils of wire lie flat on the table, on on either side of the wire. When viewed from above, the direction of the induced current is

How does the OLED produce light? (illustrate answer with energy level diagram)

A turntable of 0.8 m in diameter is spinning about its axis with an initial angular velocity of 4 rad/s. If it experiences a constant angular acceleration of 3 rad/s 2 , find: A) The angle through which the turntable has travelled from 0 sec to 2 sec. B) The arc length the turntable’s rim has travelled from 0 sec to 2 sec. C) The tangential speed of the turntable’s rim at t=2 sec. D) The tangential acceleration of the turntable’s rim at t=2sec. E) The radial acceleration of the turntable’s rim at t=2sec

A capacitor filled by dielectric slab (k=4.5) is connected to a 12.0V battery and charged up. The capacitor is then disconnected from the battery and the slab is removed.

a) Find the amount by which the potential difference across the plates changes.

b) Find the difference between the new stored energy and the original amount and specify whether this energy difference is an increase or decrease.

A rail gun uses electromagnetic forces to accelerate a projectile to very high velocities. The basic mechanism of acceleration is relatively simple and can be illustrated in the following example. A metal rod of mass 40.0 g and electrical resistance 0.200 Ωrests on parallel horizontal rails that have negligible electric resistance. The rails are a distance L = 10.0 cm apart. (Figure 1) The rails are also connected to a voltage source providing a voltage of V = 5.00 V .
The rod is placed in a vertical magnetic field. The rod begins to slide when the field reaches the value B = 7.84×10⁻² T . Assume that the rod has a slightly flattened bottom so that it slides instead of rolling. Use 9.80 m/s2 for the magnitude of the acceleration due to gravity.

Find μs, the coefficient of static friction between the rod and the rails.

Consider two point charges located on the x axis: one charge, q1= -19.0 nC , is located at x1 = -1.700 m; the second charge, q2 q= 40.0 nC , is at the origin (x = 0).

What is (F_net3)x the x-component of the net force exerted by these two charges on a third charge q3 = 54.5 nC placed between q₁ and q₂ at x₃= -1.160 m ?

Your answer may be positive or negative, depending on the direction of the force.

To get to a concert in time, a harpsichordist has to drive 122 miles in 1.93 hours. (a) If he drove at an average speed of 52.0 mi/h in a due west direction for the first 1.22 h, what must be his average speed if he is heading 30.0° south of west for the remaining 42.6 min?(b) What is his average velocity for the entire trip?(give magnitude and direction)

A thin-walled hollow cylinder with mass m₁ and radius R₁ rolls without slipping on the inner wall of a larger thin-walled hollow cylinder with mass m₂ and radius R₂ >> R₁. Both cylinders' axes are aligned and horizontal, and some magical mechanism ensures this perfect friction contact between them. Unfortunately for you, the larger cylinder rolls without slipping on a horizontal surface. Describe the motion including small oscillation frequencies near any equilibria if the systems is released from rest with the inner cylinder at some angle α₀.