Classical Mechanics Answers

The position of a particle which is constrained to move along a straight line is given by
x = 3t3 − 7t + 9 , where x is the position measured in metres from an origin and t is in seconds. Determine the acceleration of the particle when its velocity is 26 m/s.

The Niagara River delivers an average of 5470 m3 of water per second to the top of Niagara Falls, where it drops 48.5 m. If all the potential energy of that water could be converted to electrical energy, how much electrical power could Niagara Falls generate? (Note: The mass of 1 m3 of water is 1000 kg).

A mass of 3 kg is to rest vertically over a spring with a spring constant, k, of 1400 N/m. What is the energy absorbed by the spring?

A rocket of mass 14500kg accelerates at 210m/s2 for 32s from an initial speed of 5100m/s. (a) How fast will be rocket be travelling after the 32s?
(b) How much Kinetic Energy has the rocket gained?

Question 14
A radar station at O tracks two ships P & Q. P has position vector (2i + 4j) km, and Q has position vector (7i + 6j) km. What is the magnitude of the distance between ships?

A ball is left to drop, from rest, vertically from the top of a building from a position 48 m above ground.
i. What is the distance travelled by the ball after it has been falling for 3 seconds?
ii. What is the downwards velocity of the ball as it strikes the ground?

In the final stages of a moon landing, a lunar module descends under retro-thrust of its descent engine to a height h = 3.7 m above the lunar surface where it has a downward velocity of 4m/s. Calculate the impact velocity with the moon’s surface if the engine is cut off at this point and lunar gravity is 1/6 of the earth’s gravity.

Question 11
A person standing on level beach throws a ball with a velocity of 22 m/s at an angle of 30o above the horizontal. How far away is the ball when it hits the beach and what is the time of flight?

A metal rod of 10mm square cross section and length 2 m is loaded in tension with an axial tensile load of 4 kN. If the tensile modulus is 72 GPa, what will be the extension of the rod?

Two identical buggies 1 and 2 with one man in each move without friction due to
inertia along the parallel rails toward each other. When the buggies get opposite each other, the
men exchange their places by jumping in the direction perpendicular to the motion direction. As
a consequence, buggy 1 stops and buggy 1 keeps moving in the same direction, with its velocity
becoming equal to v . Find the initial velocities of the buggies 1v and 2v if the mass of each buggy
(without a man) equals M and the mass of each man m.