Inematics of particles, motion on a friction less rod, springs

[jjm09001]

Homework Statement

a 12-lb collar is attached to a spring anchored at point C and can slide on a friction-less rod forming a 30 degree angle with the vertical. The spring has constant k and is unstretched when the collar is at A. Knowing that the collar is releasted from rest at A, develop an equation to determine the velocity of the collar at point B for a given value of k such f(k)=v

Homework Equations

f=ma
w=mg

The Attempt at a Solution

not a clue. i am new at physics forums...is no attemped solution OK? apologies in advance.

 

[mark726]

Hello,

No problem, everyone has to start somewhere!

To solve this problem, we can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. We can also use the equation w = mg, where w is the weight, m is the mass, and g is the acceleration due to gravity (9.8 m/s^2).

First, we need to find the force acting on the collar at point A. Since the collar is at rest, the net force must be equal to 0. We know that the weight of the collar is 12 lbs, so we can set up the following equation:

F = ma
12 lbs = m * 0
m = 0

This tells us that the mass of the collar is 0, which doesn't seem right. However, we need to remember that the collar is attached to a spring, which will provide a force to counteract the weight of the collar.

Now, we need to consider the spring. We know that the spring has a constant k and is unstretched at point A. This means that the force it provides at point A is 0.

At point B, the spring will provide a force that is directly proportional to the displacement of the collar from point A. This can be represented by the equation F = kx, where F is the force, k is the constant, and x is the displacement.

Since the collar is released from rest, we can use the equation v^2 = u^2 + 2as to find the velocity at point B. In this case, the initial velocity (u) is 0, the acceleration (a) is provided by the spring, and the displacement (s) is equal to the length of the rod (since the collar starts at A and ends at B).

Therefore, our equation becomes:

v^2 = 0 + 2(k/m)s

Since we know that m is equal to 0, we can simplify this to:

v^2 = 0

This tells us that the velocity at point B is 0, which makes sense since the collar is at rest at point A and the spring hasn't had a chance to act on it yet.

In summary, we can say that the equation to determine the velocity of the collar at point B for a given value of k is:

v =