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For all following parts the mass of the block is 2 kg, the spring constant is 5 N/m, and you have stretched the spring an additional length of 10cm and let it go at t=0 sec. (c) Find the frequency of oscillation. (d) Find the amplitude of oscillation. (e) Find the phase. (f) What is the total energy in the spring when the block is at its lowest point?

For all following parts the mass of the block is 2 kg, the spring constant is 5 N/m, and you have stretched the spring an additional length of 10cm and let it go at t=0 sec. (c) Find the frequency of oscillation. (d) Find the amplitude of oscillation. (e) Find the phase. (f) What is the total energy in the spring when the block is at its lowest point?

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter6: Energy Of A System
Section: Chapter Questions
Problem 19P: A light spring with spring constant 1 200 N/m is hung from an elevated support. From its lower end...
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Please answer question 3 parts d, e, and f, the previous parts are answered

Que stion Given : a At' equilibrium, weig ht. Iw) of the thie restorng force (Fy) 'is balanied bj the Mass Of the biocu=M blocu Spring consi nt = K ニつ Fy +W= o =7 -ky = mg. Relaxed lenyth =L => Y = mg (2) The free end of the where Y. 15 distane the ceirny +he of the block fro when at spring then artached rest to the ce iling.so. that. the . m is the mass of the block the accelerution block is hanging verticully K is the Spriny constent ü) in ar+ の to Y stretched' +o'y the spring is part (6) stretcued additionaly and in the spring From Newton's fy.こkY the. to tal Fg :(kY +ky) ·Znd.law: F:ma so. spring force acting F: F-mg =)ma = F ng こ sub cquation 4 3: where Fs in. Cししation is the spring force ma = -KY = ky -mg From equetion li) =? ma. =mg.-kY -~g - -KY have ng.= we こ7 maこーuy (iv) the. block. is oscillating about point.X. C) relation betwcen frequency. LF) and. spring Constat (K): (5 NIM) lzug) 2ャ ニ7e- 252 Hz 5 of 5
Transcribed Image Text:Que stion Given : a At' equilibrium, weig ht. Iw) of the thie restorng force (Fy) 'is balanied bj the Mass Of the biocu=M blocu Spring consi nt = K ニつ Fy +W= o =7 -ky = mg. Relaxed lenyth =L => Y = mg (2) The free end of the where Y. 15 distane the ceirny +he of the block fro when at spring then artached rest to the ce iling.so. that. the . m is the mass of the block the accelerution block is hanging verticully K is the Spriny constent ü) in ar+ の to Y stretched' +o'y the spring is part (6) stretcued additionaly and in the spring From Newton's fy.こkY the. to tal Fg :(kY +ky) ·Znd.law: F:ma so. spring force acting F: F-mg =)ma = F ng こ sub cquation 4 3: where Fs in. Cししation is the spring force ma = -KY = ky -mg From equetion li) =? ma. =mg.-kY -~g - -KY have ng.= we こ7 maこーuy (iv) the. block. is oscillating about point.X. C) relation betwcen frequency. LF) and. spring Constat (K): (5 NIM) lzug) 2ャ ニ7e- 252 Hz 5 of 5
3. This problem is in preparation for solving the bungee jumper problem. A block of mass m is attached to spring of constant k and relaxed length L. The free end of the spring is then attached to a ceiling so the block is hanging vertically. (a) Find the distance the block is from the ceiling when at rest hanging from the spring. (b) You pull the block down an additional length y, so it has been stretched a total distance of y mg and then you let go. i. Draw a FBD of the block and write down Newton's 2nd Law for the block, do not substitute Fs -kx yet! %3D ii. Break down the stretched length of the spring into two parts. One part should be the distance from part a, and the other should be any additional stretch we add to the spring. iii. Now sum your forces with the spring force in 2 pieces. You should get a cancellation. iv. What point is the block oscillating about? For all following parts the mass of the block is 2 kg, the spring constant is 5 N/m, and you have stretched the spring an additional length of 10cm and let it go at t=0 sec. (c) Find the frequency of oscillation. (d) Find the amplitude of oscillation. (e) Find the phase. (f) What is the total energy in the spring when the block is at its lowest point?
Transcribed Image Text:3. This problem is in preparation for solving the bungee jumper problem. A block of mass m is attached to spring of constant k and relaxed length L. The free end of the spring is then attached to a ceiling so the block is hanging vertically. (a) Find the distance the block is from the ceiling when at rest hanging from the spring. (b) You pull the block down an additional length y, so it has been stretched a total distance of y mg and then you let go. i. Draw a FBD of the block and write down Newton's 2nd Law for the block, do not substitute Fs -kx yet! %3D ii. Break down the stretched length of the spring into two parts. One part should be the distance from part a, and the other should be any additional stretch we add to the spring. iii. Now sum your forces with the spring force in 2 pieces. You should get a cancellation. iv. What point is the block oscillating about? For all following parts the mass of the block is 2 kg, the spring constant is 5 N/m, and you have stretched the spring an additional length of 10cm and let it go at t=0 sec. (c) Find the frequency of oscillation. (d) Find the amplitude of oscillation. (e) Find the phase. (f) What is the total energy in the spring when the block is at its lowest point?
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