Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.60 m . The merry‑go‑round is spinning at 16.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.

During a solar eclipse, the moon, earth and sun all lie on the same line, with the moon between the earth and sun. Define your coordinates so that the earth and moon lie at greater x values than the sun. For each force, give the correct sign as well as the magnitude. (a) What force is exerted on the moon by the sun? (b) On the moon by the earth? (c) On the earth by the sun? (d) What total force is exerted on the sun? (e) On the moon? (f) On the earth?

A ball of mass 0.440 kg moving east ( + x direction) with a speed of 3.8 m/s collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

Explain the phase shift in Lock in Amplifier

A hand-driven tire pump has a 2.00 cm diameter piston and a maximum stroke of 32.0 cm.

(a) How much work do you do in one stroke if the average gauge pressure is 2.40 ✕ 10⁵ N/m² (about 35 psi)? (You may consider this an isothermal process.)
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(b) What average force do you exert on the piston, neglecting friction and gravity?
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A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 35 m/s2 for 32 s, then runs out of fuel. Ignore any air resistance effects.

1. What is the rocket's maximum altitude?

2. How long is the rocket in the air before hitting the ground?

Using the alligator clip wires, attach the coil with more loops to the galvanometer. Look carefully at the direction that the wires are turned. The idea here is that you will be moving the pole of a magnet closer to the coil— increasing the magnetic field strength in the vicinity of the coil, which is one way to increase magnetic flux.

Experiment 2: , but move the magnet much faster. What happens to your current (as measured by the meter) as you move the magnet faster? Why? More current means more electrical energy. Where does this “extra” energy come from?

from my ATMO class

Suppose you are about to begin a rafting trip through the Grand Canyon. A guide unrolls your inflatable raft on the grass next to the river and pumps air into the raft until it becomes nice and firm. The raft is then placed onto the cold water of the Colorado River and is anchored to a tree by a rope. A short time later you notice that the raft has lost its firmness and has become “baggy”. A whiner in your group cries “Oh no! There is a hole in our raft. I’m not going!” But you say “Don’t worry the raft lost its firmness because it was put in the cold water.”  Use the kinetic model to explain why the raft would lose its firmness. In your answer you should relate the kinetic model explanation for the changes in the movement of gas molecules to what happens to the temperature and number density of the air in the raft after being placed in the cold water.

For a summer job you take a position as an accident investigator for your local police force. On your first day you are called to the scene of a possibly minor accident at a large intersection with a 4-way stop. From the positions of the cars you can see that driver A was traveling northward in a small car and driver B was traveling eastward in a car that looks like it has approximately twice the mass of car A. The debris from their collision is in the center of the intersection. You can see the 5 m long marks left by the skidding tires that lead from the impact point to where the cars now rest, stuck together. The skid marks point in a direction 18.4˚east of north. From your measurements of the marks and from knowing something about the frictional force of asphalt on tires, you estimate that the cars were moving about 20 miles per hour immediately after the collision. Driver A says that driver B ran through a stop sign. Driver B says the opposite. You determine the speeds that each driver was traveling to help determine who is at fault. Make sure that y explain clearly how you determined the speeds of each car.

Light of wavelength 600 nm passes though two slits separated by 0.25mm and is observed on a screen 1.1m behind the slits. The location of the central maximum is marked on the screen and labeled y = 0. A very thin piece of glass is then placed in one slit. Because light travels slower in glass than in air, the wave passing through the glass is delayed by 5.0

A simple pendulum consists of a particle of mass m suspended by a long, massless wire of length L. Draw a free body diagram for the pendulum bob corresponding to a moment when the bob is located an angular displacement Φ away from (eg. to the right of) equilibrium. Determine an expression in terms of m, g, and Φ for the component of the net force on the bob that points tangent to the path of the bob.

Assume that the pendulum bob undergoes small angular displacements from equilibrium, meaning sinΦ = tanΦ= Φ (radians). Simplify your expression for the tangential component of the net force and use Newton's Second Law to write down the resulting differential equation of motion for the angular position Φ(t) of the pendulum bob as a function of time. Explain how your differential equation of motion implies that the pendulum undergoes simple harmonic motion, and determine the frequency of motion in terms of the given parameters.

A particle of mass 9.794

5. A plastic rod of finite length carries a uniform linear charge Q = 10 μC along the x- axis, with the left edge of the rod at the origin (0, 0) and its right edge at (4, 0) m. All distances are measured in meters.

   1. (a) Determine the net electric field at a
      point P (10,0) m, along the positive x-axis.

   2. (b) Apply integral methods to find the x- and y-components of the electric field vector due to this charged rod at the point P2 (0, 3) m, along the y-axis.

   3. (c) If the right end of the uniformly-charged rod were extended to an infinite distance along the positive x-axis, determine the magnitude and direction of the net electric field at point P(0,3) m.

Problem 12.82

A 45kg figure skater is spinning on the toes of her skates at 1.1rev/s . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40kg , 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kgeach, 71cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder.

Part A

What is her new rotation frequency, in revolutions per second?

A highway curve with a radius of 750 m is banked properly for a car traveling 120 km/h. If a 1600- kg Porshe 928S rounds the curve at 230 km/h, how much sideways force must the tires exert against the road if the car does not skid?