Mechanics | Relativity Answers

a car travelling with a speed of 2.7 meters per second changes its speed to 4.9 m/sec within 3 seconds. compute acceleration and distance

8. a) A particle of mass 4.0 kg, initially moving with a velocity of 5 . 0 ms with a particle of mass 6.0 kg, initially moving with a velocity of 5.0ms− 1 collides elastically -8.0 ms-1. What are the velocities of the two particles before and after the collision in the centre of mass frame of reference? What are the velocities of the two particles after the collision in the laboratory frame?

b) A 30.0 kg girl stands at the rim of a merry-go-round that has a moment of inertia of 2 500 kg m and a radius of 3.00 m. The merry-go-round is initially at rest. The woman then starts walking around the rim clockwise at a constant speed of 2 . 0 ms-1 ,i) In what direction and with what angular speed does the merry-go-round rotate? ii) How much work does the girl do to set herself and the merry-go-round into motion

a) An L-shaped object of uniform density is hung over a nail so that it is free to rotate. Determine the angle that the long side of the object makes with the vertical. The long side of the L-shaped object is given to be twice as long as the short side.
b) A solid cylinder rolls up an inclined plane without slipping. If the incline makes an angle of 30º to the horizontal and the coefficient of static friction is µs = 0.40 , find its acceleration. Also determine the angle of the inclined plane at which the object will start to slip.

6. a) The distance between the oxygen molecule and each of the hydrogen atoms in a water (H2O) molecule is 0.96 Å and the angle between the two oxygen-hydrogen bonds is 105°. Treating the atoms as particles, find the centre of mass of the system.


b) A stationary ball, with a mass of 0.2 kg, is struck by an identical ball moving at .4ms −1 After the collision, the second ball moves 60° to the left of its original direction. The stationary ball moves 30° to the right of the moving ball’s original direction. What is the velocity of each ball after the collision?

a) A force F=(x÷a-1) is acting on a particle along the x-axis. Determine the work done by the force in moving the particle from x=0 to x=2a.


b) A block of mass 6.0 kg slides from rest at a height of 2.0 m down to a horizontal surface where it passes over a 1.5 m rough patch. After crossing this patch it climbs up another incline which is at an angle of 30° to the ground. The rough patch has a coefficient of kinetic friction . µk=0.25 What height does the block reach on the incline before it comes to rest?

a) What is the maximum torque exerted by a 60 kg person riding a bike, if the rider puts all his weight on each pedal when climbing a hill? The pedals rotate in a circle of radius 17
b) A ball of mass 1.5 kg rolling to the right with a speed of ,6.31ms−1 collides head-on with a spring with a spring constant of .0.22Nm−1 Determine the maximum compression of the spring and the speed of the ball when the compression of the spring is 0.10 m

3. a) A ball has an angular velocity of 1s 0.5 rad−1counterclockwise. Some time later, after rotating through a total angle of 4.5 radians, the ball has an angular velocity of 1s 5.1 rad−1 clockwise. Determine the angular acceleration, the average angular velocity and how much time it takes for the ball to attain this velocity.
b) When a high diver wants to execute a flip in midair, she draws her legs up against her chest. Why does this make her rotate faster? What should she do when she wants to come out of her flip?

Write the equation of motion of a simple harmonic oscillator which has an amplitude of
5 cm and it executes 150 oscillations in 5 minutes with an initial phase of 45°. Also
obtain the value of its maximum velocity.

When a high diver wants to execute a flip in midair, she draws her legs up against her
chest. Why does this make her rotate faster? What should she do when she wants to
come out of her flip?

A 2400 W engine pulls a 200 kg block at constant speed up a 12.0 m long, 25.0° incline.
Determine long does it takes to cover this distance.