I THINK SOMEONE HAS THIS SAME QUETION! A massless spring of constant k = 91.0 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance of d. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5 m. The entire track and the loop-the-loop are frictionless, except for the section of track between points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is µk = 0.24, and that the length of AB is 2.5 m, determine the minimum compression d of the spring that enables the block to just make it through the loop-the-loop at point C. [Hint: The force of the track on the block will be zero if the block barely makes it through the-loop-the-loop.]
Assuming point C is at the top, then
g= v^2/r so you have to calculate v at the top.
So energy at the bottom must equal KE at the top + the change in PE to get to the top
RequiredKEbotom= 1/2 m*vtop^2+mg(2r)
Now, you have losses before you get there due to friction, mu*mg*2.5, so that has to be added to get the initial KE at the spring.
PEspring= mu*mg*2.5+1/2m vtop^2+mg(2r)
PE spring= 1/2 k d^2, solve for d.
thank you, but i am exteremly confused! so i just use PE spring to find d?
i guess i'm just confused on the mu means static friction? .24?
is mu friction? .24?
Blah
To find the minimum compression d of the spring that enables the block to just make it through the loop-the-loop at point C, we need to analyze the forces acting on the block at different points along the track.
At point A, the block is pressed against the spring and is about to be released. The spring force Fs acting on the block is given by Hooke's Law: Fs = k * d.
As the block moves from A to B, it experiences the force of kinetic friction fk and the force of gravity mg. The net force on the block in this section is the difference between these two forces: fk - mg.
To determine the force of kinetic friction, we can use the coefficient of kinetic friction µk. The force of kinetic friction fk is given by fk = µk * normal force, where the normal force is equal to the magnitude of the gravitational force acting on the block: normal force = mg.
Therefore, fk = µk * mg.
At point B, the block reaches the minimum height within the loop-the-loop, and the normal force becomes zero. The block just loses contact with the track at this point.
To calculate the minimum compression d of the spring that enables the block to pass through the loop-the-loop, we need to find the compression distance at which the net force on the block is zero.
At point B, the net force on the block is given by: fk - mg = 0.
Substituting the expression for fk, we have: µk * mg - mg = 0.
Simplifying: (µk - 1) * mg = 0.
Since µk is given as 0.24, we can solve for mg: 0.24 * mg - mg = 0.
Simplifying further: -0.76 * mg = 0.
This implies that mg = 0, which is not possible. Thus, there is no minimum compression d that enables the block to make it through the loop-the-loop. The block will not be able to reach point C without additional forces acting on it.