Simple Harmonic Motion: Determine Velocity at t=0.250s

AI Thread Summary
The discussion revolves around calculating the velocity of a 39.8 g oscillating mass at t=0.250s using the position equation x(t) = (2.00cm)cos(5t - 4.00π). The correct formula for velocity is V_x = -ωA sin(ωt + φ), where the user initially miscalculated the velocity due to unit conversion errors. After clarification, it was noted that the velocity should be expressed in cm/s instead of m/s. The key takeaway is the importance of unit consistency in calculations. Understanding the relationship between velocity and position is crucial for solving harmonic motion problems effectively.
Moe*
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_{}b]1. Homework Statement [/b)

The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00\pi) where t is in seconds. Determine Velocity at t= 0.250s

M= 39.8 g
T= 1.2575 rad/s
K= 9.95e-1 N/m
initial postion= 2 cm

Homework Equations



V_{x}= -\omegaAsin(\omegat + \phi)

The Attempt at a Solution



the attempt i just substitued
V_{x}= -5 rad/s*2sin( 5.00(0.250)-4\pi)... but this didn't work and i don't understand why?
 
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for the the equations posted its supposed to be V subscript x= wAsin(wt + phi) and x(t) = (2.00cm)cos(5t - 4pi)
 
Moe* said:
The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00\pi) where t is in seconds. Determine Velocity at t= 0.250s

What is the basic relation connecting velocity and position of any particle? Use that.
 
Moe* said:
_{}b]1. Homework Statement [/b)

The position of a 39.8 g oscillating mass is given by the equation x(t)= (2.00cm)cos(5t- 4.00\pi) where t is in seconds. Determine Velocity at t= 0.250s

M= 39.8 g
T= 1.2575 rad/s
K= 9.95e-1 N/m
initial postion= 2 cm

Homework Equations



V_{x}= -\omegaAsin(\omegat + \phi)

The Attempt at a Solution



the attempt i just substitued
V_{x}= -5 rad/s*2sin( 5.00(0.250)-4\pi)... but this didn't work and i don't understand why?
it seems work to me...
 
Your right it does work, i guess I entered in the wrong units when i answered the question( m/s instead of cm/s).
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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