Q2: (a) A particle of mass m moves under the influence of the force F = a(sinwtî + coswtſ). Ifthe particle initially at rest at the origin. Prove that work done at any time t is given byW =mw?=(1– coswt) and that the instantaneous power applied is -sinwt.ma?(b)Find the moment of inertia of a ring of radius a about an axis through its center.

Name: Q2: (a) A particle of mass m moves under the influence of the force F
Uploaded: 2024-03-20T06:57:25.000Z
Channel: Bartleby
Description: Q2: (a) A particle of mass m moves under the influence of the force F = a(sinwtî + coswtſ). Ifthe particle initially at rest at the origin. Prove that work done at any time t is given byW =mw?=(1– coswt) and that the instantaneous power applied is -

Here given a particle of mass m moves under a influence of force. It initially at rest. We have to…

Science

Physics

Q2: (a) A particle of mass m moves under the influence of the force F = a(sinwtî + coswtj). If the particle initially at rest at the origin. Prove that work done at any time t is given by -(1- coswt) and that the instantaneous power applied is sinwt.

Q2: (a) A particle of mass m moves under the influence of the force F = a(sinwtî + coswtj). If the particle initially at rest at the origin. Prove that work done at any time t is given by -(1- coswt) and that the instantaneous power applied is sinwt.

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter9: Momentum And Its Conservation

Section: Chapter Questions

Problem 1STP

See similar textbooks

Similar questions

A long, thin rod of mass m = 5.00 kg and length = 1.20 m rotates around an axis perpendicular to the rod with an angularspeed of 3.00 rad/s. a. What is the angular momentum of therod if the axis passes through the rods midpoint? b. What is theangular momentum of the rod if the axis passes through a pointhalfway between its midpoint and its end?
A solid sphere of radius 10 cm is allowed to rotate freely about an axis. The sphere is given a sharp blow so that its center of mass starts from the position shown in the following figure with speed 15 cm/s. What is the maximum angle that the diameter makes with the vertical?
A 5.00 kg disk of radius 1.20 m initially rotated at 2.00 rad/s relative to a fixed axis passing through its center of mass. Then 3.00 J of work is then added to the system. What will be the final kinetic energy of the disk? The moment of inertia of a disk of mass M and radius R is 1/2 MR^2.
A position vector of a particle of 2kg mass at any time t is given byr(t) = 3ti+ 2t^2j+ t^3kFind at t = 1s,a) velocity and acceleration vectors,b) the torque on the particle,c) the kinetic energy,d) Power,e) Find the work done on the particle between t = 0 and t = 1s
A figure skater rotating at 3.4 rad/s with arms extended has a moment of inertia of 2.97 kg ∙ m2. If he pulls in his arms so his moment of inertia decreases to 1.9 kg ∙ m2, what is the final Kenetic energy?
Prove that the moment of inertia of a solid sphere of uniform density, when rotating around a diameter,is 2MR2/5, where M is the mass of the sphere and R is the radius.Hint: integrate the infinitesimal volume element in spherical coordinates.
A metal can containing condensed mushroom soup has mass 215 g, height 10.8 cm, and diameter 6.38 cm. It is placed at rest on its side at the top of a 3.00-m-long incline that is at 25.0° to the horizontal and is then released to roll straight down. It reaches the bottom of the incline after 1.50 s. (a) Assuming mechanical energy conservation, calculate the moment of inertia of the can. (b) Which pieces of data, if any, are unnecessary for calculating the solution? (c) Why can’t the moment of inertia be calculated from I = (1)/(2) mr2 for the cylindrical can?
Prove that the moment of inertia of a solid cylinder of uniform density, when rotating around its central axis,is MR2/2, where M is the mass of the cylinder and R is its radius. Hint: integrate the infinitesimal volume element in cylindrical coordinates
While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. (a) Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900 kg.m, the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. (b) How much work is done if the leg rotates through an angle of 20.0 with a constant force exerted by the muscle?
A cord is wrapped around the rim of a solidcylinder of radius 0.25 m, and a constantforce of 40 N is exerted on the cord shown,as shown in the following figure. Thecylinder is mounted on frictionlessbearings, and its moment of inertia is6.0 kg ⋅ m2. (a) Use the work energytheorem to calculate the angular velocity ofthe cylinder after 5.0 m of cord have beenremoved. (b) If the 40-N force is replacedby a 40-N weight, what is the angularvelocity of the cylinder after 5.0 m of cordhave unwound?
A thin rod of length L is falling freely in horizontal position from a height H above the surface of the table, in such a way that the end of the rod just hits the edge of the table. This collision is instantaneous and totally elastic (i.e. the mechanical energy is conserved). At what time after the collision does the rod perform a whole revolution? Where is its centre at that moment? (H = 80 cm, L = 10 cm)
On a frictionless table, a m = 0.70kg glob of clay strikes a uniform M = 0.82kg bar perpendicularly at a point b = 0.49m from the center of the bar and sticks toit. The bar is L = 1.22 m long and the clayis moving at v = 5.50 m/s before strikingthe bar.What is the final speed of the center ofmass?At what angular speed does the bar/claysystem rotate about its center of mass after the impact?