Mechanics | Relativity Answers

A block of mass 5 kg is on a tabletop (which we will assume for the moment is frictionless) A string tied to the block runs over a pulley and is tied to a 2 kg block hanging below the pulley
a) How much gravity force acts on the 5 kg block? Does this cause any motion?
b) How much force acts on the 2 kg block? Does this cause any motion?
c) How much force actually causes things to move?
d) How much mass is being moved ?
e) How much acceleration occurs?
f) How much force must be acting in the string where it is tied to the 5 kg block?
g) Now repeat the whole thing assuming that a friction force of 5 N. Acts to slow everything down.

A child of mass 30 kg skates down from the top of a ramp having a constant slope of
15 degree. The child’s speed increases from 1.5m/s to 3.0m/s as she reaches the
bottom of the ramp. A force of kinetic friction of magnitude 50 N opposes her
motion. Draw the appropriate force diagram and determine the length of the ramp.
Take g = 10m/s2

The box having mass “m” is being pulled by a motor.Initial velocity of the box is V0.Motor pulles the box by force F=500s+550,where “s” is the distance the box is pulled (meters),and force is in newtons.Define the velocity and acceleration of the box as a function of distance ‘s’.If the motor has efficiency of “E(epsilon)=0,65” ,power input required to be supplied by the motor as a function of distance.

Can a object moving at constant speed accelerate. Explain your answer

Two laser pointers are placed at a distance 2Lo apart along x-axis in the optical lab. frame. At a particular moment in time, the lasers point out light simultaneously (named events A and B), which cross at the midway point (named event C), and then arrive simultaneously at the opposite side (named event D and E).

(a) Draw a spacetime diagram of the events in the optical lab reference frame. Draw the worldlines of the laser pointers and the light rays. Mark all five events and draw lines of simultaneity connecting events A and B, and events D and E.

(b) Draw a spacetime diagram of the situation in a moving frame with velocity v = +βc relative to the laboratory. Draw all the worldlines, events and the lines of simultaneity that connect events A and B, and events D and E.

(c) Given that the slope of worldlines in (b) is -2 and the slope of lines of simultaneity is -1/2. Draw both reference frames on a single spacetime diagram.

A cannonball is dropped from the top of a building. If the point of release is 105 ft above the ground, what is the velocity of the cannonball just before it strikes the ground?

A weightless rod CD, 1.0m long is acted upon by horizontal forces of 2N, 4N, 8N is shown in the figure. What force will be necessary to produce equilibrium?

Consider a mirror clock and a light pulse is released inside of the clock. The clock is then move by someone at speed v. Shows that time dilation, t’, in a moving frame as viewed by someone at rest as

t' = t/√(1-v^2/c^2)

State the postulates of Special Theory of Relativity and the Equivalence Principle.

A child standing on the floor of a balcony of a multi storey building, throws a ball straight upwards with an initial velocity of 10m/s. Assume the the floor is 25m high from the ground. Take g=9.8m/s/s.find the
a) maximum height above the ground reached by the ball.
B.) velocity with which the ball strikes the ground.

2.
A 10kg trunk lies on a horizontal rough floor,the coefficient of friction between the trunk and the floor is 0.75. Calculate magnitude of force P which is necessary to pull the trunk horizontally if the P is applied horizontally and at 30 degrees above the horizontal.

3.
A particle of mass 300g is attached to one end of a light inextensible string of length 40cm, the other end of the string being fixed at 0 on a smooth horizontal surface. If the particle describe a circle centre o, find the tension in the string when
A)The speed of the particle is 2.83m/s.
B)The angular speed of the particle is 5rad/s.