Classical Mechanics Answers

A certain oscillator satisfies the equation of motion: 𝑥••+ 4x = 0. Initially the particle is at

the point x = √3 when it is projected towards the origin with speed 2.

2.1. Show that the position, x, of the particle at any given time, t, is given by:

x = √3 cos 2t – sin 2t.

The energy stored in a copper wire of cross sectional area 0.5mm² is 0.04J. calculate the force applied to it if its length is 2m. Take young modulus of copper as 1.2×10¹¹Nm^-2.

A string is stretched by 5cm. If a mass of 1kg is dropped from a height of 0.3m onto a spring whose force constant is 400Nm^-¹. Calculate the maximum distance the spring will be compressed

A roller coaster which weighs 640 lb starts from rest at point A and begins to coast down the track. If the frictional force is 5.0lb, how fast will the coaster be going at point B, which is 100 ft down the track and 30 ft below point A, and at point C, which is 50 ft farther along the track and 20 ft higher than point B?

Motion under inverse square law force derivation

The image above is a neat copy of a photo of an electricity meter for a domestic solar array. The display shows the energy we sold to the electricity company on a winter's day. Between 7 a.m. and 5 p.m., how many kilowatt hours did this household sell to the electricity company? E =

E= _____ kW.hrs

. Give your answer to two significant figures.

Each box is 100 W 

high and 1 hr 

wide.

Determine the magnitude of an electric field at r=0.01 m from the center of non-conducting sphere with a radius of R=0.001m possessing a charge of 7C which evenly distributed throughout the sphere. (r>R).

Solve for the electric flux that acts on a uniform electric field with a magnitude of 8000N/C approximately passes through a 10m^2 flat surface area.

a molecules of oxygen possess a charges of -2C and 2C separated from a distance of 0.2m. Calculate the dipole moment in this condition.

The depth of the crater of a Volcano was calculated in the following manner. From a helicopter flying vertically upwards at 20 feet per second, a small bomb was released at the instant the helicopter was 120 feet above the crater surface. The sound of the explosion was heard 9 seconds later. The speed of the sound is 1000 fps. What is the depth of the crater in feet?