Classical Mechanics Answers

A light inextensible string of lenght l has one end attached to the end A of a smooth heavy rod AB whose lenght is 2a.The other end of the string is attached to a small smooth ring C (whose weight may be neglected) which slides over the rod.The rod is suspended with the string over a smooth peg P. Show that, in the position of equilibrium
(i) The portion PC of the string is at right angles to the rod.
(ii)The length x of the portion PA is given by the equation
l((x^2)+(a^2))=2x^3 .

A 5.0kg, 60cm diameter disk rotates on a axle passing through one edge. The axle is parallel to the floor. The cylinder is held with the center of mass at the same height as the axle,then released.

1) what's the cylinders initial angular acceleration?

2) What is the cylinders angular velocity when it is directly below the axle?

Please assist

A 200g ball is dropped from a height of 2.0m, bounces on a hard floor and rebounds to a height of 1.5m and the interval for total travel is t= 5.0 ms.

What maximum force(Fmax) does the floor exert on the ball?

Please assist

A hydroelectric power plant uses spinning turbines to transform the kinetic energy of moving water into electric energy with 80% efficiency ( 80% kinetic energy becomes electric energy).

A small hydroelectric plant at the base of the dam generates 50 MW of electric power when the falling water has a speed of 18 m/s.

What is the water flow rate - kilograms of water per second through turbines?

Please assist.

A) How much work must you do to push a 10kg block of steel across a steel table at a steady speed of 1.0 m/s for 3.0 s?

B) What's the power output while doing so?

A person pulls a box along the ground at a constant speed. If we say Earth and the box as our system, what can we say about the net external force on the system?

Three children are sitting on a seasaw in such a way that it balances. A 20kg and 30kg boy are on opposite sides at a distance B and 3B , respectively from the pivot. The rod is held horizontal and then released. Find its angular acceleration at the instant it is released.

A 4000kg lunar lander is in orbit 50km above the surface of the moon. It needs to move to a 300km high orbit in order to link up with the mother ship that will take the astronauts home. How much work must the thrusters do?

Dan is gliding on his skateboard at. 4, 0m/s. He suddenly jumps backwards off his skateboard, kicking the skateboard forward at 8,0 m/s. How fast is Dan going as his feet hit the ground? Dan's mass is 50kg and the skateboards mass is 5,0kg.

Which statement best describes the relationship between matter and energy in the universe?
1 : Changes of mass to energy and energy to mass are observable in all chemical reactions.
2 : The sum of mass and energy in the universe is increasing over time
3 : Matter and energy can be converted from one to the other, but their sum stays constant.
4 : The sum of mass and energy in the universe is decreasing over time