Mechanics | Relativity Answers

A 1200 kg station wagon is moving along a straight highway at 120 m/s. Another car, with

mass 1800 kg and speed 20 m/s, has its centre of mass 40 m ahead of the centre of mass of

the station wagon. Find the position of the centre of mass of the system consisting of the

two automobiles. Find the magnitude of the total momentum of the system. Find the speed

of the system using the speed of the centre of mass.

A ball is thrown forward horizontally from the top of a cliff with a velocity 10ms-1. The

height of the cliff above the ground is 45m. Calculate (i) the time to reach the ground (ii)

the distance from the cliff of the ball on hitting the ground (iii) the velocity with which

the ball hits the ground. (iv) the direction of the ball to the horizontal just before it hits

the ground

•Q2. the position of a particle moving along the x-axis is given by

                                x= 7.8 + 9.2t -2.1 t3  

Where x is in meters and t is in seconds.

a). What is the velocity at t=3.5s?

b). Is the velocity constant or continuous?

c). What is the displacement of the particle after 3.5 seconds?

d). Sketch   i. displacement - time graph

                    ii. Velocity – time graph

                    iii. Acceleration-time graph

For the particle motion within the time o ≤ t ≤ 6s

A particle of mass 3 Kg falls from rest at a point 5 m above the surface of a liquid which is in a container. There is no instantaneous change in speed of the particle as it enters the liquid. The depth of the liquid in the container is 4 m. The downward acceleration of the particle while it moving in the liquid is 5.5 m/s^2. (i) Find the resistance to motion of the particle while it is moving in the liquid. (ii) Sketch the velocity- time graph for the motion of the particle, from the time it starts to move until the time it reaches the bottom of the container. Show on your sketch the velocity and the time when the particle enters the liquid, and when the particle reaches the bottom of the container.

A car of mass 350 Kg is travelling at 30 m/s when it starts to slow down, 100 m from a junction. At first, it slows just using the air resistance of 200 N then, at a distance of s m from the junction, it slows using brakes, providing a force of 2000 N as well as the air resistance. Find the distance from the junction at which the brakes must be applied if the car is to stop at the junction.

A diver of mass 60 Kg dives from a height of 10 m into a swimming pool. Through the air there is resistance of 50 N a) Find the speed at which the diver enter the water b) Once in the water, the water provides an upward force of 2000 N. Find the greatest depth in water the diver reaches.

An inclined plane as shown in figure 1 is used to raise an object of mass 30 kg. If the plane is

inclined 5° above the horizontal and the coefficient of friction is 0.20, calculate the ideal

mechanical advantage, actual mechanical advantage, and the efficiency of this machine.

For the system of two blocks on a frictionless double incline where the blocks are linked by an inextensible massless string over a frictionless pulley (see figure),

A. Draw the free body diagram for m1 and m2.

B. Express the equations of motion of the two blocks using Newton's Laws.

C. Prove that for the system to be in equilibrium.

Consider a spacecraft moving at 0.95c travelling past an observer on Earth. The said observer and the occupant of the ship each start identical alarm clocks set to ring after 15 hours. With respect to the observer on Earth, at what time will the Earth clock read when the spacecraft clock rings? 

The resultant of the two forces has a magnitude of 650 N. Determine the direction of the resultant and the magnitude of P