h t t p : / / i m g 2 0 5 . i m a g e s h a c k . u s / i / c a p t u r e b b . j p g /
i am stuck on part c
how do i find work with out using the spring constant
work equals force parallel times displacement at which the force is acted during...
Work done by spring = .5 kx^2
Work = delta K
but delta K = 0 because the table top is frictionless
Work = delta U
delta U = 0 in this situation correct?
so I'm stuck...
i think it might be zero but .5 kx^2 would not give zero now would it...
thanks
wait how do i find out the spring constant?
Stuck
To find the work without using the spring constant, you need to consider the given information and formulas.
First, let's break down the problem. You have a table top that is frictionless, and you are considering the work done on the system.
The work done by a force is given by the formula:
Work = Force × Displacement × cos(θ)
In this case, you mentioned that the table top is frictionless, so there is no external force acting on the system other than the force exerted by the spring.
Since the displacement occurs only in the x direction, the angle θ between the force and displacement vectors is 0 degrees. Therefore, cos(0) = 1, and we can simplify the formula to:
Work = Force × Displacement
Now, according to Hooke's Law, the force exerted by a spring can be expressed as:
Force = k × displacement
Substituting this into the work formula, we get:
Work = (k × displacement) × displacement
= k × displacement^2
So, the general formula for work done by a spring is:
Work = k × displacement^2
In your case, if you're trying to find the work without using the spring constant, you can use the fact that the change in kinetic energy (delta K) is zero because the tabletop is frictionless. This means that the work done by the spring must be equal to the change in potential energy (delta U) of the system.
delta U = Work done by the spring
Since delta U is zero (as mentioned in your question), it implies that the work done by the spring is also zero. Therefore, regardless of the value of the spring constant (k) or the displacement (x), the work done by the spring in this situation would be zero.
To summarize,
Work done by the spring = 0
I hope this explanation helps you understand how to approach solving the problem.