How can I calculate the potential energy stored in a compressed spring?

AI Thread Summary
To calculate the potential energy stored in a compressed spring, the work done on the system must be understood in terms of the applied force and displacement. The work done on block A is equal to its kinetic energy, but this does not directly represent the work done on the entire system, which includes the spring. The relevant equation for work is the force applied multiplied by the displacement. The discussion clarifies that the potential energy can be derived from the net external work done on the system without needing to partition it into kinetic energy and elastic potential energy. Ultimately, the calculation simplifies to using the force and displacement directly.
dge
Messages
4
Reaction score
2
Homework Statement
Two identical blocks, A and B, on a frictionless surface are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t1 to t2, block A is pushed through a distance dA by a hand exerting a force of magnitude FA, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left.

Write an expression for the net external work done on system ABS by external forces in terms of given quantities (ie. FA, dA, and/or t2). Explain.
Relevant Equations
Work = Force * displacement
I feel like I've gotten stuck on this. I know the work done is equal to the kinetic energy of block A, but I can't figure out how I would find the potential energy stored in the spring without using the spring constant in the equation. W = FA * dA + U
 
Physics news on Phys.org
dge said:
Homework Statement:: Two identical blocks, A and B, on a frictionless surface are connected by a spring of negligible mass. The spring is initially unstretched. During the interval from t1 to t2, block A is pushed through a distance dA by a hand exerting a force of magnitude FA, as shown. Block B is held in place by a wall. The wall exerts a force on block B that varies with time but is always directed to the left.

Write an expression for the net external work done on system ABS by external forces in terms of given quantities (ie. FA, dA, and/or t2). Explain.
Relevant Equations:: Work = Force * displacement

the work done is equal to the kinetic energy of block A,
That’s the work done on block A, but it is not the work done on the system "ABS" (S presumably being the spring).
You do not need to care how the work done on the system gets partitioned into KE and EPE.
 
haruspex said:
That’s the work done on block A, but it is not the work done on the system "ABS" (S presumably being the spring).
You do not need to care how the work done on the system gets partitioned into KE and EPE.
So would it just be the force applied * the displacement?
 
dge said:
So would it just be the force applied * the displacement?
Yes.
 
Reply
  • Like
Likes dge and Delta2
haruspex said:
Yes.
I guess I overcomplicated that in my head. Thank you!
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
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

Find elastic energy in the compressed spring.
Replies
12
Views
3K
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
2K
Problem with when to use Force and Energy. What compresses spring/
Replies
3
Views
1K
Calculating the spring force constant K
Replies
14
Views
2K
Why is my method for finding the spring constant incorrect?
Replies
17
Views
3K
Why can we move the spring with constant speed when we apply a force?
Replies
29
Views
2K
A block dropping onto a spring system
2
Replies
58
Views
2K
Energy stored in a double spring system
Replies
17
Views
1K
2 Carts on a Track Compressed by a Spring -- What are their Velocities?
Replies
3
Views
2K
Spring compression -- Ball colliding with a spring-mounted platform
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top