Classical Mechanics Answers

Determine the equation of motion of an oscillation in a U tube

A planet is revolving around the sun as shown in the figure. The radius vectors joining the sun and the planet at points A and B are 90×10^6 km and 60×10^6 km respectively. The ratio of velocities of the planet at A and B when its velocities make 30° and 60°with major axis of the orbit is
Ans 1/√3

The I.Sc lecture theatre of a college is 40 ft wide and has a door at a corner. A teacher enters at 12.00 noon through the door and makes 10 rounds along the 40 ft wall back and forth during the period and finally leaves the classroom at 12.50 p.m. through the same door. Compute his average speed and average velocity.

An oscillating pendulum bulb has a mass 0.1kg. It's amplitude is 0.01 meter and it's period is 2sec. The constant w (omega) in the acceleration formula is?

Three people are moving with velocity v , 2v and 3v respectively. They see rain falling at angles alpha , beta and gamma respectively. What is the relation between alpha beta and gamma ?

A spherical billiard ball of uniform density has mass m and radius R , and moment of inertia about the center of mass Icm = (2 / 5)mR^2. The ball, initially at rest on a table, is given a sharp horizontal impulse by a cue stick that is held an unknown distance h above the centerline. The force applied by the cue to the ball is sufficiently large that you may ignore the friction between the ball and the table during the impulse (as any pool player knows). The ball leaves the cue with a given speed v0 and an angular velocity w0. Because of its initial rotation, the ball eventually acquires a maximum speed of (9/7)v0.

a) Briefly explain why angular momentum is conserved about any point along the line of contact between the ball and the table after the impulse.
b) Use conservation of angular momentum about any point along the line of contact between the ball and the table, and your results from part a), to find the ratio h / R.

A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth surface. A block B placed at the top of the wedge takes a time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, what will happen to the block?

A block of mass m is placed on a smooth wedge of inclination theta. The whole system is accelerated horizontally so that the block does not slip on the wedge. What is the magnitude of force exerted by the wedge on the block?

Figure beside shows a vertical spring mass system. The springs are identical with
spring constant k and original length L. The mass is slightly displaced along the
horizontal direction. Neglect gravity and obtain the equation of motion of the mass
for small oscillation along the horizontal direction. Give a schematic plot of the
corresponding potential. What happens to the potential if the mass is displaced
along vertical direction?

A car is travelling on a road. The maximum velocity the car can attain is 24 m/s & the maximum deceleration is 4 ms^-2. If car starts from rest and comes to rest after traveling 1032 m in the shortest time of 56 s, the maximum acceleration that the car can attain is?