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(II) A block of mass $m$ is attached to the end of a spring (spring stiffness constant $k ),$ Fig. $35 .$ The mass is given an initial displacement $x_{0}$ from equilibrium, and an initial speed $v_{0}$ . Ignoring friction and the mass of the spring, use energyFIGURE 35 Problems $23,37,$ and 38

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A) $\sqrt{v_{0}^{2}+\frac{k}{m} x_{0}^{2}}$B) $\sqrt{x_{0}^{2}+\frac{m}{k} v_{0}^{2}}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

02:57

(II) A block of mass $m$ i…

01:12

0:00

(III) A block of mass m is…

04:12

02:31

'(III) A block of mas…

02:26

A block of mass 2.5 kg sl…

06:53

(III) A spring $(k=75 \mat…

03:49

(II) An object with mass 3…

05:37

In FIGURE 8-46 a 1.2-kg bl…

01:16

A block of mass $m=0.60 \m…

06:30

(II) A 6.620 -kg wood bloc…

03:20

The block of mass $m$ is a…

06:04

A block with mass 0.50 $\m…

04:34

Two objects of masses $m_{…

01:59

A $0.40-\mathrm{kg}$. mass…

04:24

(I) A mass $m$ is attached…

Figure (8-E7) shows a spri…

block off Mass. Amazon passed to the end of the spring. So I'll drive dagger off the situation first. So we have. But this isn't the UN stress position right now, and it is gonna force constant gate. The mass is given an initial displacement. So well, stretch the mask. Some displacement here. And the displacement is X not. And a disposition. The block has given some velocity of you. Not so it time will come when the blockers release that the block is going to go to good point off maximum stretch, which is X max, and it is going to oscillate back and forth in simple harmonic oscillator. So our disposition, the energy is kinetic energy send. It is no stretch dislocation here. The energy is Canada. Bless. We have elastic potential energy on a dislocation. We have only elastic potential energy. And in part one, it's a CZ. You need to find out an equation for the max speed. So we need to see and wish location. We have the max speed. It's very obvious that the max speed is that this location because the only energy of the block here it says this is candidate energy and energy is not shared with any potential energy. So therefore, what we can do is that we can equate the energy one with energy too. So total energy at one you know is e one is equal to the total energy at two, which is you too. So energy one is equals two. The kinetic energy bitches equals to half M b Max squid and energy to which is the energy or dislocation is equals to have and Venus squared less Half came It's not square. If you solve that half and half pencils from all the sides and we are left with an equation M v Max squad is equals to em Venus squired, escape extorted, squared Since we need to find an equation for VUE Max, we divide the entire thing. But I am And our equation is V Max is equals two. I just write V Max. There's equals to a square root off. We not squared as again. See, Eminem cancels vino Dsquared. Bless Cabe. I am ex not squared. So that is our equation for V Max. All right. For part two, it says I need to find an equation for the maximum stretch So in this case, you know, we need to equate the energy at location to and location three. So hee too is equals two. Petri at 82 will have the energy half M V, North squared less half and key X squared. This is three. And at e three, we have the maximum stretch, which is equal to have game if X Max Quaid again have and 1/2 gassed from both the sides. I need to find an equation for ex Max squared so we can divide this whole equation by him. But first of all, and to simplify the question and be no risk wired plus kxan disquiet is equals. Two key ex Max squared divide this whole equation by K. And they get an equation. Ex Max squared These equals to extort squared because the scale and the scale cancel this one and we just left over with I am by K V Nord Square. So therefore, equation is ex Max is equal to squire route off. Excellent squared. Yes. And by K being r squared

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