Classical Mechanics Answers

A trough of length 6 ft has for its vertical cross section an isosceles trapezoid. The upper and lower bases are 6 ft and 2 ft respectively and the altitude is 2 ft. If the trough is full of water, find the force on the slant side of the trough.

A plate in the shape of a triangle is submerged vertically and the base which is 3 ft long is in the surface of the water. Find the altitude of the triangle if the force due to the water pressure against the face of the plate is 50w where w is the weight per cu. ft. of water.

A rectangular plate 12 ft long and 8 ft wide is submerged vertically with the longer edge in the surface of the water. Find the force on one side of the plate.

X=5t^2 - 2t. Find the velocity at t=3s

tX=5

a particle is moving under the influence of an attractive Force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities u and v parallel to n axes of x and y,it will not strike the axis of x unless u>v²k² and that in this case the distance of the point of impact from the origin is uk²/√(u-vk)

Two blocks, each of mass m, Are connected by an extentionless, uniform string of lengh l. One block is placed on a smooth horizontal surface, and the other block hangs over the side. The string passing over the frictionless pulley. Describe the motion of the system

a) When the mass of the string is negligible

b) when the string has a mass m.

Please assist.

1. A dodgem car of mass 200 kg moves with a velocity of 3 m/s. The moving dodgem collides with a stationary one of mass 180 kg.

After the collision, the 200 kg dodgem continues to move in the same direction at a speed of 1 m/s.

Calculate the speed v with which the 180 kg (second) dodgem moves to the right after the collision.

1. In a game of bowls one particular bowl hits the jack head on causing it to move forward. The jack has a mass of 300 g and was originally stationary.  The bowl has a mass of 1 kg and was moving at a speed of 2 m/s before hitting the jack, but continued forwards at 1.5 m/s after the collision.  What is the speed of the jack after the collision?

1. Police suspect that a van was breaking the speed limit when it collided with a parked car. Investigations provided them with the following data: mass of parked car   = 800 kg,  mass of van = 1000 kg,  velocity of  car after collision = 5 m/s,  velocity of van after collision = 11 m/s

Show whether the van was breaking the 30 mph speed limit (equivalent to 13 m/s

1. During an experiment, a vehicle, mass 400 g, is pushed so that it runs along an air track with a velocity of 2.0 ms^-1. It collides with a stationary vehicle, mass 600 g, which moves on with a velocity of 1.6 ms^-1

Find the velocity of the 400 g vehicle after the collision.

1. A 2kg trolley travelling at 3 m/s hits a stationary 1kg trolley.  After the collision the 2kg trolley continues to travel in the same direction at 1 m/s. 

The 1 kg trolley moves off separately. 

Calculate the velocity of the 1kg trolley after the collision.

1. A truck of mass 2000kg, moving at 20m/s, collides with a car of mass 1000kg, which is stationary. What is the velocity of the car after the collision if the truck now moves 

forward at 10m/s ?

1. A skater of mass 70 kg is moving at 4 m/s when he bumps into a skater of mass 50 kg who is not moving.  They move off together on the ice.  What is their velocity immediately after the collision?

The boy in question 1 now throws his ball horizontally out of a high window with a velocity of 3.1 m s-1. How long will it take to reach the ground 18m below?