Mechanics | Relativity Answers

Graham,aphysicsenthusiast,isaskedbyhisinstructortovisitanearbycarpentry. Heobserved there a hand–held powered reciprocating saw, say a sabre saw, which performs SHM in a vertical plane with an angular frequency of 350rads−1. Assume that the tip of the toothed blade of the saw is at x = 0 with positive velocity when t = 0 and the amplitude of SHM is 2.40cm. Write an equation, as a function of time, which shows the position of the tip of the toothed blade. Also calculate that how much will the blade take to travel from x = 0 to x = 1.20cm? To 2.40cm?

Sketch the orbit described by r = kθ, k is a constant and find the force law for a
central force field that govern this motion.

Define what is a central force and describe 3 main characteristics of the motion dynamics resulting from such type of force. List 5 distinctive examples of central forces with their origin and characteristics.

Find the divergence and curl of vector F
F=2xyzi+3xyj-bzk

find the magnitude of vectorF =2i+3j+5k and also calculate the angles of vector makes with x-axis, y-axis and z-axis

Calculate the size of the stellar aberration effect in Newtonian physics for
light coming straight down at speed c and a telescope moving straight
sideways at speed v. At what angle θ must we point the telescope to see
the star? Hint: In what direction is the light moving in the reference frame
of the telescope? Express θ in terms of v and c.

(a) Twelve equal charges, q, are situated at the corners of a regular 12–sided polygon (for in-
stance, one on each numeral of a clock face). What is the net force on a test charge Q at the center?
(b) Suppose one of the 12 q’s is removed (the one at “6 o’clock”). What is the force on Q?
Explain your reasoning carefully
(c) Now 13 equal charges, q, are placed at the corners of a regular 13–sided polygon. What is the
force on a test charge Q at the center?
(d) If one of the 13 q’s is removed, what is the force on Q? Explain your reasoning.

In an experiment, the tiny droplets of the negatively electrified oil are dropping through a vac-
uum. Magnitude of the electric field is 5.92 × 104 N C−1
. Direction of the electric field is assumed to be
downward. (a) An experimenter observes a one particular droplet and that droplet remains suspended against
gravity. Assume the mass of the droplet to be 2.93 × 10−15 kg. What is the charge carried by the droplet? (b)
Now another droplet of same mass falls, in the vacuum, from rest to 15.3 cm in 0.275 s. What is the charge
on the droplet in this case?

Graham, a physics enthusiast, is asked by his instructor to visit a nearby carpentry. He observed
there a hand–held powered reciprocating saw, say a sabre saw, which performs SHM in a vertical plane with
an angular frequency of 350 rad s−1
. Assume that the tip of the toothed blade of the saw is at x = 0 with
positive velocity when t = 0 and the amplitude of SHM is 2.40 cm. Write an equation, as a function of time,
which shows the position of the tip of the toothed blade. Also calculate that how much will the blade take to
travel from x = 0 to x = 1.20 cm? To 2.40 cm?

A sledge moving over a smooth horizontal surface of ice at a velocity drives out on a horizontal road and comes to a halt as shown. The sledge has a length l, mass m and friction between runners and road is .