I need help with b... I found that k=.750880 for part a but I can't figure out what y would be to get potential energy.
A 52 g mass is attached to a massless spring and allowed to oscillate around an equilibrium according to:
y(t) = 0.8 * sin( 3.8 * t ) where y is measured in meters and t in seconds.
(a) What is the spring constant in N/m?
k = .750880 N/m
(b) What is the Total Energy in the mass and spring in J?
E = ???J
HELP: The total energy is the sum of the kinetic energy and potential energy. At what point in the motion is the energy all kinetic? At what point is it all potential? Can you compute it at this point?
HELP: Kinetic energy is 1/2 * Mass * v2
Potential energy is 1/2 * k * y2
We know that at the mass's maximum y-position it has zero velocity, so simply compute Potential Energy at that point.
At equilibrium position, K.E.=max,P.E. = 0
At the two extreme points, K.E.=0,P.E.=max
Total energy is constant at ANY POINT.
We find E at extreme point.
E = 1/2*k*(0.8)^2
= 0.24J
but you know the velocity
dy/dt = .8 * 3.8 cos (3.8 t)
maximum velocity when sin (3.8 t) = 1
si
max Ke = total = (1/2) (.052)(.8*3.8)^2
lol, both method can find the answer
To find the potential energy at the maximum y-position, we need to determine the value of y at that point. In the given equation, y(t) = 0.8 * sin(3.8 * t), the maximum value of sin(3.8 * t) would be 1. Therefore, at the maximum y-position, y(t) = 0.8 * 1 = 0.8 meters.
Now, we can use the formula for potential energy: PE = 1/2 * k * y^2.
Substituting the given value of k = 0.750880 N/m and y = 0.8 m into the formula, we get:
PE = 1/2 * 0.750880 N/m * (0.8 m)^2
= 1/2 * 0.750880 N/m * 0.64 m^2
= 0.24028416 Nm = 0.240 J (rounded to three decimal places).
Therefore, the potential energy at the maximum y-position is 0.240 J.