Answer:
The magnitude of the force is 1.29*10^-3N in the positive x direction
Explanation:
In order to calculate the magnitude and direction of the force, you take into account that the force is the space derivative of the potential enrgy, as follow:
(1)
where:
You replace the expression for U into the equation (1) and solve for F:
![F(x)=-\frac{d}{dx}[Ax^4]=-4Ax^3](https://tex.z-dn.net/?f=F%28x%29%3D-%5Cfrac%7Bd%7D%7Bdx%7D%5BAx%5E4%5D%3D-4Ax%5E3)
(2)
The force on the particle, for x = -0.080m is:
The magnitude of the force is 1.29*10^-3N in the positive x direction
When the entire group of forces acting on an object is balanced,
the individual forces all add up to zero, and the effect on the object
is the same as it would be if there were no force at all acting on it.
No force on it means no acceleration ... no change in speed or
direction of motion.
No change in speed or direction of motion means constant velocity.
The initial kinetic energy of the cart is
(1)
where m is the mass of the cart and v its initial velocity.
Then, the cart hits the spring compressing it. The maximum compression occurs when the cart stops, and at that point the kinetic energy of the cart is zero, so all its initial kinetic energy has been converted into elastic potential energy of the spring:
where k is the spring constant and x is the spring compression.
For energy conservation, K=U. We can calculate U first: the compression of the spring is x=60 cm=0.60 m, while the spring constant is k=250 N/m, so
So, the initial kinetic energy of the cart is also 45 J, and from (1) we can find the value of the initial velocity:
Answer:
This is the midline or the medium which is the exact middle of the graphs minimum and maximum points(which are the amplitude)
