Ballistic Pendulum help (Finding the height)?
The length of the pendulum is unimportant. (kinetic energy) KE = (1/2)mv^2 (potential engery)PE = mgh (momentum) p = mv Total energy is conserved in a collision, so is momentum. KE of bullet before = (1/2)(.012)(380)^2 = 1444 N I assume the bullet and pendulum "stick" after collision, so that m = 6.012kg KE of bullet+pedulum = 1444N directly after collision. Now the pendulum swings and converts all the KE into PE mgh = 1444 => h = 1444/(6.012 * 9.8) = 24.51m
Physics: Displacement of Pendulum Problem?
You have to approach this problem in two steps: 1) conservation of momentum 2) conservation of energy First: Calculate the velocity of the pendulum , by conservation of momentum: Total momentum before = total momentum after (0.022*250) + (0*5.4) = V2 ( 5.4+0.022) 5.5 / 5.422 = V2 V2 = 1.014 The pendulum will move with a velocity of 1.014m/s Calculate the kinetic energy of the pendulum: Ek = ½*m*v² Ek = ½*5.422*1.014² Ek = 2.79J This kinetic energy is all converted into gravitaional potential energy when the pendulum swings to its highest point: Ep = m*g*h 2.79 = 5.422 * 9.8*h h = 2.79/5.422*9.8 h = 0.052m vertical displacement of pendulum The pendulum will have a vertical displacement of 0.052m or 52mm
How do you find the height displacement of a pendulum?
Draw he geometry out. When the pendulum is hanging the length in the VERTICAL direction is L When the pendulum is displaced at an angle theta, the length in the VERTICAL direction is L*cos(theta) Therefore, the change in height from the bottom of the swing to the top of the swing in the VERTICAL direction = L - L*cos(theta) height = L*(1-cos(theta))
The oscillation of a pendulum is assumed to be underdamped oscillation which means the wave of a pendulum is in exponential decay.The maximum distance reached by a wave is the amplitude.Pushing a pendulum is applying an impulsive force F.The resultant of pushing the pendulum, is the factor of the impulsive force and the original max. displacement amplitude ( F*A or F*x), which accounts for the extra work done (W) from a free vibration (leaving it alone) to a forced vibration (one that has an external force).Taking into account the impusive force in the equation solution to the differential equation of vibratory motion gives the difference in displacement.Equation of vibratory motion= ma-kx-damping=0.Solution to vib.equation= x (t)= ((F*e^(damping constant*natural angular acc*time))/ mass*underdamped angular acc) * sin (underdamped angular acc. * time)
Determine its maximum angular displacement.?
b) max displacement let θ(m) be maximum angular displacement let h be height above mean level, L= length h = [L - L cos θ(m)] energy conservation T Energy (θ=0, h=0) = T energy (θ = θ(m)) PE1 + KE1 = PE2 + KE2 0 + 0.5 *mv^2 = mgh + 0 (stops) 0.5 *mv^2 = mg [L - L cos θ(m)] 0.5 *6.75* (1.36)^2 = 6.75*9.8*1.53[1 - cos θ(m)] 0.5 *(1.36)^2 = 9.8*1.53[1 - cos θ(m)] [1 - cos θ(m)] = 0.0617 cos θ(m) = 1 - 0.0617 = 0.9383 θ(m) = 20.23 degree
PLZ HELP!!!=( Pendulum-Bullet problem!?
Okay so first you should use conservation of momentum m1v1 = (m1+m2)v2 Where m1 = mass of bullet m2 = mass of pendulum v1 = bullet velocity we solve for v2, which is the velocity of the pendulum after the bullet strikes v2 = (m1v1)/(m2+m1) = (.0196)(244)/(3.56+.0196) = 1.336 m/s So then we use conservation of energy, to find the max height the pendulum can rise. mgh = ½mv² where m cancels out g = 9.8 m/s² v = v2 = 1.336 m/s we want to solve for h h = ½v²/g h = ½(1.336)²/(9.8) h = .09107 m so now that we have the vertical displacement, we can use the length of the string to find the horizontal displacement. I wish I could draw you a picture for this part, but you will just have to look at my work and see if you can reason for yourself why I did what I did. The horizontal displacement is given by x = √[L² - (L - h)²] where L = length of string = 2.66 m h = .09107 m x = √[2.66² - (2.66 - .09107)²] x = √[2.66² - 2.56893²] x = √0.476199 x = 0.690071 m
If you know the velocity at the bottom of the swing, you can find the amplitude using energy conservation. When the particle is stopped at the top of its swing it has no kinetic energy so all of its energy is potential. Likewise, when the particle is at the bottom of the swing it has no gravitational potential energy and all of its energy is kinetic.[math]mgh_{max}=\frac{1}{2}mv^2[/math]The height above the base of the pendulum is [math]h_{max}=l(1-cos \theta_{max} )[/math].Now we have:[math]mgl(1-cos \theta_{max} )=\frac{1}{2}mv^2[/math][math]\rightarrow 1-cos \theta_{max} =\frac{v^2}{2gl}[/math][math]\rightarrow 1-\frac{v^2}{2gl}=cos \theta_{max}[/math][math]\rightarrow \theta_{max}=cos^{-1}\big(1-\frac{v^2}{2gl}\big)[/math].If you want to find the maximum displacement horizontally then[math]x_{max}=l sin\theta_{max}[/math].
Do you mean height above ground or the length of the pendulum?If the former, nothing, no impact.If the latter the cycle time is a function of the pendulum length so longer pendula will cycle slower.
To find the maximum velocity of a pendulum, how do you derive the formula for the height?
Draw an arc of circle of radius 0.66 m, with one radius in vertical direction and the other at the left at angle of 12 degree from the vertical. In the vertical radius mark a point which is equal to 0.66 cos 12 from the center of the arc of the circle. ( A horizontal line drawn from the highest point passes through this point) The height through which the pendulum has raised is (0.66 - 066 cos 12.) h = 0.66 (1-cos 12) = 0.014m. Use this height to find the medium speed using, mgh = 0.5 m v^2. Or simply v^2 = 2gh. The physics behind this formula is the pendulum is raised to height of h from the equilibrium position. At this point it has a potential energy of mgh. As it falls it looses its P.E and gains K.E At the equilibrium position all its P.E is converted to K.E and hence it has maximum speed at this position. Also mgh = ½ mv^2.
This question can be solved in many different ways. Lets solve it by applying energy conservation principle.Let us assume “u “is the initial velocity.Let us also assume that Potential energy at the point of projection to be 0.Then.. Total energy of the ball at point of projection =kinetic energy +potential energy=1/2mu^2Let the maximum height attained be h. So applyin mechanical energy conservation for the two points that is the point of projection and the maximum height we get=> 1/2mu^2=mghSolve for “h"U will geth=u^2/2g.And this is the maximum height attained.