Ball and rod, finding when compression force=0

In summary, the problem involves a ball fixed to a rod of negligible mass and length L. When released from rest at an angle of θ=0, the compression force in the rod becomes zero at a certain angle θ as the ball falls. This is due to the decrease in the normal reaction on the ball and the increase in centripetal force. By using tangent-normal coordinates and considering the forces involved, the relation between Ρ, h, and cosθ can be found to determine the angle at which the compression force becomes zero.
  • #1
jromega3
27
0

Homework Statement


the ball has a mass M and is fixed to a rod having a negligible mass and length L. If it's released from rest when theta=0, determine the angle theta at which the compression force in the rod becomes zero.


Homework Equations



A(tangent) = dv/dt = vdv/ds
A (normal) = v^2p ...where p is radius of curvature, or L.




The Attempt at a Solution


well, I'm stumped. This is dynamics problem more so than physics, but still.
I have a FBD with mg down and the C force.
I used tangent-normal coordinates, and have the Compression force in the normal direction.
So I get A=V^2 / L
I guess I just don't get conceptually why the force would ever need to become zero?

PS...so theta is from the vertical axis down.

So it starts completely vertical and makes its way down clockwise.
 
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  • #2
As the rod falls, the compressional force is mg*cosθ. This force provides the necessary centripetal force for the ball to remain on the rod. As θ increases this force decreases, the normal reaction on the ball decreases and centripetal force on the ball increases. When theses two forces are equal normal reaction is zero and there is no compressional froce on the rod.
Since the ball is falling freely v^2 = 2gh.
Now draw the diagram, and find the relation between Ρ, h and cosθ.
 
  • #3


As a scientist, it is important to understand the theoretical concepts behind the problem before attempting to solve it. In this case, we are dealing with a ball and rod system where the ball is fixed to a rod of negligible mass and length L. The ball has a mass M and is released from rest at an angle of 0 degrees. Our goal is to determine the angle at which the compression force in the rod becomes zero.

Firstly, we need to understand what compression force means in this context. When the ball is released, it will start to rotate due to the force of gravity acting on it. As it rotates, the rod will start to experience a compression force due to the weight of the ball. This force will increase as the angle theta increases, reaching a maximum when the ball is at its lowest point (theta = 90 degrees). After that, as the ball continues to rotate, the compression force will decrease until it becomes zero at a certain angle.

To determine this angle, we need to consider the forces acting on the ball and rod system. We have the weight of the ball (mg) acting downwards and the normal force from the rod acting upwards. At the point where the compression force becomes zero, the normal force must be equal and opposite to the weight of the ball. This means that the ball is in equilibrium, and the sum of all forces acting on it is zero.

Using this information, we can set up an equation for the sum of forces in the vertical direction:

mg - N = 0

Where N is the normal force. We can also use the equation for the normal acceleration in terms of angular velocity (A(normal) = v^2/L) to relate the normal force to the angular velocity of the ball.

Now, we can solve for the angle theta at which the compression force becomes zero by setting the normal force to zero and solving for theta:

mg = 0
A(normal) = v^2/L = 0
v = 0

This means that at the angle where the compression force becomes zero, the ball must have zero velocity. Solving for theta, we get:

tan(theta) = v/0 = 0

This means that theta = 0 degrees, which is the initial angle at which the ball is released. Therefore, the compression force in the rod becomes zero when the ball is at its initial position (theta = 0 degrees).

In conclusion, as a scientist, it is important
 

1. What is a ball and rod?

A ball and rod refers to a simple mechanical system that consists of a ball and a rod, where the ball is attached to one end of the rod and the other end is fixed. The system is commonly used to demonstrate principles of mechanics in physics experiments.

2. How can you find when the compression force equals 0?

The compression force equals 0 when the ball and rod system is in equilibrium, meaning that all forces acting on the system are balanced and there is no net force. This can be found by using the equation F = kx, where F is the compression force, k is the spring constant, and x is the displacement of the ball from its equilibrium position. When F = 0, x will also equal 0, indicating that the system is in equilibrium.

3. What factors affect the compression force in a ball and rod system?

The compression force in a ball and rod system is affected by the spring constant of the rod, the mass of the ball, and the displacement of the ball from its equilibrium position. The spring constant is a measure of the stiffness of the rod, while the mass of the ball determines how much force is needed to compress the spring. The displacement of the ball also plays a role, as the further the ball is from its equilibrium position, the greater the compression force will be.

4. How does the compression force change with different materials?

The compression force in a ball and rod system will vary depending on the material of the rod and the ball. Materials with a higher spring constant, such as steel, will require more force to compress the spring, while materials with a lower spring constant, such as rubber, will require less force. The mass of the ball can also affect the compression force, as heavier materials will require more force to compress the spring.

5. What are some real-world applications of the ball and rod system?

The ball and rod system has many practical applications, such as in shock absorbers for vehicles, where the system can be used to absorb and dampen the impact of bumps in the road. It is also used in door closers, where the spring helps to close the door slowly and prevent it from slamming shut. Additionally, the system is used in engineering and construction to test the strength and durability of materials under compression forces.

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