Solving Vibrations and Waves: Mass, Spring Constant, Energy, Speed

  • Thread starter Thread starter Elvis
  • Start date Start date
  • Tags Tags
    Vibrations Waves
AI Thread Summary
A 5 kg mass attached to a spring with a spring constant of 13 N/cm, pulled back 20 cm, has a total energy of 26 joules at the moment of release. The energy is calculated using the potential energy formula, where kinetic energy is zero at the point of release. For the second scenario with a 15 kg mass and a spring constant of 20 N/cm, the speed at 5 cm is sought, with the answer indicated as 2.2 m/s. The discussion emphasizes the importance of understanding energy storage in springs and the relationship between mass, spring constant, and speed. The problem-solving approach highlights the need for clarity in energy calculations at different points in the spring's motion.
Elvis
Messages
14
Reaction score
0
1) A 5 kg mass, m, rests on a frictionless, horizontal, wooden table top, and is attached to one end of a spring anchored at its other end . If the spring has a spring constant=13 N/cm and the mass is pulled back (in the positive direction ) 20 cm and released, to the nearest tenth of a joule, what is its total energy?
2) if the mass is 15 kg and the spring constant is 20 N/cm, to the nearest tenth of a m/s, what is its speed at x= 5 cm?

I have solved the 1st one :

1N/cm=100N/m

E = PE + KE
E = 1/2kA^2 + 1/2mv^2 At KE v=0 because the mass stops momentarily as it changes directions. Then :

E = PE
E = 1/2kA^2
E = 1/2(13*100)*(0.2)^2
E = 26J

I have problem with the second problem. please help to solve this. I have 2 hours that I am tryin to solve it . I have only the answer that is 2.2m/s.

Please help......



:cry: Lol...
----------------------------------------------------------------------------------------
 
Physics news on Phys.org
The spring is still pulled back 20 cm in part (b). Can you find how much energy is stored in it at the moment of release when v = 0?
 
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}...
View full post »

Similar threads

Vibrations & Waves: Solving Mass, Spring Constant & Energy
Replies
1
Views
3K
Waves and vibrations on a string
Replies
2
Views
2K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
2K
Mass atop four springs with external input: Reduce vibration amplitude by factor of ten
Replies
3
Views
867
Question about springs and rotational/translational energy
Replies
4
Views
1K
Why can we move the spring with constant speed when we apply a force?
Replies
29
Views
2K
Energy stored in a double spring system
Replies
17
Views
1K
Spring SHM Homework: Solving for Displacement of a Suspended Point Mass
Replies
26
Views
3K
Help with this problem about a mass oscillating on a spring
Replies
1
Views
1K
Solve Horizontal Spring Homework: T, A, V&Where Max V
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top