(c) The position, in terms of time, of a block of mass 0.50 kg on a frictionless horizontal surface, atthe end of a horizontal spring which has a force constant of 1000 N/m, isx = (0.022m)cos(2nft)) Determine the total mechanical energy of the system.(ii) Determine the maximum velocity of the block.(iii) Determine the velocity of the block when x= 0.011 m.(iv) What would the graph of x = (0.022m)cos[(2nft) + represent? [Discuss the similaritiesand the differences between the two graphs ofx= (0.022m)cos(2nft) andx = (0.022m)cos[(2ft) +.(v) Draw the acceleration vs time graphs on top of cach other, ofx= (0.022m)cos(2nft) andx = (0.022m)cos[(2mft) +.Interpret what is represented graphically.

(1) Total Mechanical Energy = 12kA2 = 12×1000×0.0222 = 0.242 J

(c) The position, in terms of time, of a block of mass 0.50 kg on a frictionless horizontal surface, at the end of a horizontal spring which has a force constant of 1000 N/m, is x = (0.022m)cos(2mft) (i) Determine the total mechanical energy of the system. (ii) Determine the maximum velocity of the block. (iii) Determine the velocity of the block when x=0.011m.

(c) The position, in terms of time, of a block of mass 0.50 kg on a frictionless horizontal surface, at the end of a horizontal spring which has a force constant of 1000 N/m, is x = (0.022m)cos(2mft) (i) Determine the total mechanical energy of the system. (ii) Determine the maximum velocity of the block. (iii) Determine the velocity of the block when x=0.011m.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter16: Oscillations

Section: Chapter Questions

Problem 64PQ: Use the data in Table P16.59 for a block of mass m = 0.250 kg and assume friction is negligible. a....

See similar textbooks

Similar questions

• A 3.55-g bullet embeds itself in a 1.47-kg block, which is attachedto a spring of force constant 825 N>m. If the maximum compressionof the spring is 5.88 cm, find (a) the initial speed of the bullet and(b) the time for the bullet–block system to come to rest
A spring with a mass of 2 kg has natural length 0.5 m. A force of 25.6 N isrequired to maintain it stretched to a length of 0.7 m. If the spring is stretched to a lengthof 0.7 m and then released with initial velocity O, find the position of the mass at anytime t.
A block of mass ? = 300 g is released from rest from the top of a frictionless ramp. At the bottom of the ramp, a spring with a force constant ? = 400 N/m is fixed, as shown in the figure. If the maximum compression of the spring is 10 cm, determine the angle θ
Consider an object of mass 0.150kg that is attached to a horizontal spring of spring constant 35.2 N/m is kept on the frictionless level air track and stretched to the length of 6.50 cm.An outward initial velocity of 2.20 m/s is given to the object,so that determine the displacement of the spring between 6.50 cm and the extreme position
Consider an object on a spring whose position is given by x = (5.00cm)cos(9.90s-1t). a. Find the maximum speed of the object? When does this maximum speed first occur after t = 0? What is the maximum acceleration of the object? When does the maximum magnitude of the acceleration first occur after t = 0?
Consider a plot of the spring's compression ) as a function of the magnitude of the applied force (F) for an ideal elastic spring. The slopeof the curve would be none of the given choices Othe mass of the object attacned tot O the spring constam O the acceleration due to gravity the reciprocal of the sprng constant
A body of mass m = 2,50 kg is hung ona vertical spring of spring constant k = 90 N/m. At t = 0 the body is displaced from its equilibri-um position downward by distance x0 = 13 cm and it is given an initial velocity v0 = 78 cm/salso directed downwards.a) Give the displacement x(t) of the body asa function of time. After how much time doesthe body pass through the equilibrium positionfirst?b) Find the maximal displacement, speed andacceleration of the body during the motion. c) Find the total energy stored in the oscil-lation.
An ideal spring hangs fromthe ceiling. A 1.45 kg mass ishung from the spring,stretching the spring adistanceᵅ = 0.0855 m fromits original length when itreaches equilibrium. Themass is then lifted up adistanceᵃ = 0.0285 m fromthe equilibrium position andreleased. What is the kineticenergy of the mass at theinstant it passes back throughthe equilibrium position?
A mass of 0.75 kg is attached to a relaxed sprig with k= 2.5 N/m. The mass rests on a horizontal, frictionless surface. If the mads is displaced by 0.33 m, what is the magnitude of the force exerted on the mass by the spring?
A mass of 0.43 kg is is initially traveling at across a horizontal surface. It then reaches a spring with a fixed end having a spring constant of 138 N/m that is positioned horizontally and initially at equilibrium. If the initial speed of the mass is 3.81 as it contacts the spring, what is the speed of the mass after compressing the by 0.153 m if the coefficient of kinetic friction is between the surfaces is 0.47 ?
When firing a 1.60 kg rifle, the recoil of this can compress a spring of spring constant 3800 N/m of 2.3 cm. What is the speed of the bullet fired, knowing that it has 12.0 g mass?
When you compress a string with k=12nN/m by 5.8 cm, what is the magnitudeof the force you exert on the spring in the unit of N?