Mechanics | Relativity Answers

A particle of mass m is hanging with the help of an elastic string of unstretched length a and force constant mg/a .The other end is fixed to a peg on vertical wall. String is given an additional extension of 2a in vertical downward direction by pulling the mass and released from rest. Find the maximum height reached by it during its subsequent motion above point of release. (Neglect interaction with peg if any)

Water is pumped from a depth of 10 m and delivered through a pipe of cross section 10–2 m2 upto a height of 10 m. If it is needed to deliver a volume 0.2 m3 per second, find the power required.

A force F = − k ( x ˆ i + y ˆ j ) [where k is a positive constant] acts on a particle moving in the x-y plane.Starting from origin, the particle is taken to (a, a) and then to ( a 2 , 0. Find the total work done

A particle of mass 3 kg is rotating in a circle of radius 1 m such that the angle rotated by its radius is given by θ = 3 (t + sint). Find the net force acting on the particle when t = π/2

Speedy Sue is going to an archery range. At the range she pulls the bowstring back by exerting 0.350m by exerting a fore that will increase from nothing to 250 N uniformly. What is the spring constant of the bow? How much work does Sue do in pulling the arrow back? What is the speed of the arrow as it leaves the bow?

The outer edge of the grooved area of a long-playing record is at a radial distance 36 cm from the center; the inner edge is at a radial distance of 15 cm. The record rotates at 6.7 rev/min. The needle of the pick-up arm takes 2.3 minutes to move uniformly from the outer edge to the inner edge.
What is the radial speed of the needle?
m/s
What is the speed of the outer edge relative to the needle?
m/s
What is the speed of the inner edge relative to the needle?
m/s
Suppose the phonograph is turned off, and the record uniformly and stops rotating after 10 s. What is the angular acceleration?
rad/s2

A water wave has a speed of 23.0 meters/second. If the wave’s frequency is 0.0680 hertz, what is the wavelength?

A swimming pool is 5m long, 4m wide and 3m deep. Compute the force exerted by the water against the bottom and either end. Do not include the force due to air pressure.

A bike coasts up a long hill. The hill has an incline of 38 degrees. The mass of the bike and rider is 129kg. If the bike starts up the hill at a velocity of 10 m/s, how far will the rider go up the hill before stopping? The coefficient of kinetic friction is .30 .

A flat (unbanked) curve on a highway has a radius of 215.0 m . A car rounds the curve at a speed of 25.0 m/s .What is the minimum coefficient of static friction that will prevent sliding?Suppose that the highway is icy and the coefficient of friction between the tires and pavement is only one-third what you found in the previous part. What should be the maximum speed of the car so it can round the curve safely?