Mechanics | Relativity Answers

The angular position of a particle is given by theta(t) = b + ct + dt2, where b, c, and d are constants. The radial displacement of the particle is r (t) = a theta(t) where a is a constant. Determine (a) the angular velocity, (b) the angular acceleration alpha, (c) the linear velocity, (d) the transverse acceleration, and (e) the centripetal acceleration of the particle.

A particle describes the curve rⁿ=aⁿ cos nθ under a force p towards the
pole. Find the law of force?

Suppose that you are pushing a child on a swing, initially at rest, periodically.
(a) Draw a displacement-time graph for the resulting oscillatory motion of the swing.
(b) Is it an example of free or damped or damped forced oscillation?

An projectile is fired uphill over ground with slope at an angle alpha to the horizontal.Find the direction in which it should be aimed to achieve the maximum range

A proton is moving at 425 m/s. (a) How much work must be done on it to stop it?(answer in joules) (A proton has a mass of 1.67×10−27 kg.) (b) Assume the net braking force acting on it has magnitude 8.01×10−16 N and is directed opposite to its initial velocity. Over what distance must the force be applied?(in meters) Watch your negative signs in this problem.

A net force of 1.6×10−15 N acts on an electron over a displacement of 5.0 cm, in the same direction as the net force. (a) What is the change in kinetic energy of the electron? (b) If the electron was initially at rest, what is the speed of the electron? An electron has a mass of 9.1×10−31 kg. answer part a) in joules and part b) in meters per second.

You get paid $1.25 per joule of work. How much do you charge for moving a 10.0 kg box up to a shelf that is 1.50 meters off the ground?

What is the change in the gravitational potential energy of a Boeing 767 jet as it soars from the runway up to a cruising altitude of 10.2 km? Assume its mass is a constant 2.04×10[sup]5[/sup] kg. answer in joules.

A small domestic elevator has a mass of 454 kg and can ascend at a rate of 0.180 m/s. What is the average power that must be supplied for the elevator to move at this rate? answer in Watts.

The equation of motion of a particle moving along the x-axis is given by:
d[sup]2[/sup]x/dt[sup]2[/sup]+4dx/dt+8x=20cos2t

Calculate the amplitude, period and frequency of the oscillation after a long time has elapsed.