A 2.6kg laboratory cart is given a push and moves with a speed of 2.0m/s toward a solid barrier, where it is brought to rest by a spring bumper. How much energy will be stored in the spring (elastic potential energy) at the moment when the spring is fully compressed? What is the average force exerted by the spring if it is compressed 0.12m? (Why is it necessary to specify average force in this situation?)

Question

anonymous · Answer

(1) The kinetic energy of the cart.
(2) The work done by the spring on the cart is the change in its kinetic energy (Work-Energy Theorem), which you know from (1). You could estimate the average force by $W=F_{avg}\Delta x$, where $W$ is the work done by the spring.

beth12345 · Answer

what's the change in x stand for?

beth12345 · Answer

$$\Delta x$$?

anonymous · Answer

delta x stands for change in the length of the spring!

anonymous · Answer

were u able to understand?

beth12345 · Answer

not really

anonymous · Answer

what is the kinetic energy of cart first?

anonymous · Answer

take the cart and the spring as the system,the forces between them will be internal,net external force on the system is zero so u can use principle of conservation of energy

anonymous · Answer

initial mechanical energy of the system=final ME

anonymous · Answer

now try to frame the equation

beth12345 · Answer

$$Ek=1/2 \times g \times h$$ $$=1/2 \times 2.6kg \times 2m/s ^{2}$$$$=5.2 J$$

anonymous · Answer

yes u got it right,now what's the potential energy stored in the spring initially?

beth12345 · Answer

would it be the same? since Ek=Ep?

anonymous · Answer

do u know the expression for potential e stored in a spring?

beth12345 · Answer

no

anonymous · Answer

its (1/2)*k*x^2
where k=spring constant of the spring, x=compession or elongatian from natural length

anonymous · Answer

initially the spring is not elongated or compressed, so what's theEp stored in it initially?

beth12345 · Answer

0?

anonymous · Answer

one point to be corrected: k.e=1/2*m*v^2 correct that beth

anonymous · Answer

yes

anonymous · Answer

mechanical energy= Ep+Ek
so what's the initial MEof the system?

beth12345 · Answer

5.2J

anonymous · Answer

yes
now tke the final situation when the spring is fully compressed
and calculate the finalME of the system and then apply principle of COE

beth12345 · Answer

i don't really know what the spring constant is

anonymous · Answer

ok no problem
what will happen to the cart when spring is fully comprsd?

beth12345 · Answer

it will bounce back?

beth12345 · Answer

or collect potential energy?

anonymous · Answer

yes it will,but that's not what we r luking for
we r interstd at the moment wen spring is fully cprsd

anonymous · Answer

it will collect PE only wen it has lost all of its Ek to the spring

anonymous · Answer

so wat wud be the Ek of the cart at that particular moment?

beth12345 · Answer

oh would it be 0 since the velocity is 0?

anonymous · Answer

yes exactly now conside the PE of the spring and useCOE to get PE

anonymous · Answer

the final ME of the system is only due to thePE of the spring
now this is what COE says
initialME=fialME
use this equation

beth12345 · Answer

what does ME and COE stand for again?

anonymous · Answer

ME=mechanical energy(Ep+Ek)
COE=conservation of ME

beth12345 · Answer

would the answer be 5.2J fir the fianal ME

anonymous · Answer

yes

anonymous · Answer

and as i mentioned earlier finalME is due to the potential energy stored in the spring

beth12345 · Answer

ok, thank you :)

anonymous · Answer

there is one more way to solve this q and that is by using work energy theorem

beth12345 · Answer

ok, ill try that later but right now I have to catch my bus, thank you so much for helping me out :)

anonymous · Answer

ur welcome:)