Dynamics Problem (rigid body)

In summary: Your Name]In summary, the problem involves finding the tension in cable A immediately after cord B is cut. Using the equation F = ma, we can set up an equation with the weight of the object and the tension in cable A. Solving for the acceleration and then plugging it into the equation, we can find the tension in cable A to be 58.86 N.
  • #1
pconn5
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0
Not really sure if this is where this should be but oh well.

Homework Statement


Image attached.

It is given that:

b = 200 mm
mass = 6 kg

Find the tension in cable A immediately after cord B is cut.


Homework Equations


Moment = I*alpha + m*a*d
F = ma?


The Attempt at a Solution


I tried to do
Moment about A = I*alpha (second part is zero?) , so 9.81*6*.1 = 1/6*6*2*.2^2*alpha

I then solved for alpha.

And plugged it into:
Moment about G(center) = I*alpha, but this is wrong and I don't really understand why to be honest with you. It trips me up when the forces are not perpendicular to the center for some reason.

The final answer is T = 23.5 N.

Thanks.
 

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  • #2


Hello there,

Thank you for posting your question in this forum. I am happy to help you find the tension in cable A after cord B is cut.

To solve this problem, we need to use the equation F = ma, where F is the net force acting on the object, m is the mass of the object, and a is the acceleration of the object. In this case, we are interested in finding the tension in cable A, which is the net force acting on the object.

First, let's consider the forces acting on the object before cord B is cut. We have the weight of the object, which is equal to its mass (6 kg) multiplied by the acceleration due to gravity (9.81 m/s^2). This results in a force of 58.86 N acting downwards.

Next, let's consider the forces acting on the object after cord B is cut. We still have the weight of the object acting downwards, but now we also have the tension in cable A acting upwards. This tension is the net force acting on the object, since there are no other forces acting on the object in the vertical direction.

Now, we can set up the equation F = ma and solve for the tension in cable A. We know that the mass of the object is 6 kg and the acceleration is unknown, so we can rewrite the equation as T = 6a. We also know that the net force acting on the object is equal to the weight of the object (58.86 N), so we can set up the equation T = 58.86 N.

Solving for a, we get a = 58.86/6 = 9.81 m/s^2. This is the acceleration of the object after cord B is cut.

Finally, we can plug this value of acceleration into our equation T = 6a to find the tension in cable A. This results in T = 6(9.81) = 58.86 N. This is the final answer for the tension in cable A immediately after cord B is cut.

I hope this explanation helps you understand the problem better. If you have any other questions, please feel free to ask. Good luck with your studies!
 

1. What is a rigid body in dynamics?

A rigid body is an object that maintains its shape and size while undergoing motion. This means that all of its points move in the same direction and distance, and the distances between these points remain constant. In other words, a rigid body does not deform or change shape when it moves.

2. How do you solve a dynamics problem involving a rigid body?

To solve a dynamics problem involving a rigid body, you typically use Newton's laws of motion and the equations of rotational motion. These equations describe the relationships between forces, mass, acceleration, and torque (rotational force) in a system. By analyzing these equations and applying them to the specific problem, you can solve for unknown variables such as acceleration, velocity, and position.

3. What types of forces can act on a rigid body?

There are two types of forces that can act on a rigid body: external forces and internal forces. External forces are those that act on the object from outside, such as gravity, friction, or applied forces. Internal forces are those that act within the object, such as tension or compression forces within its structure.

4. How does the mass distribution of a rigid body affect its dynamics?

The mass distribution of a rigid body can affect its dynamics in several ways. For example, if the mass is distributed unevenly, it can cause the body to rotate or have an uneven acceleration. Additionally, the moment of inertia, which is a measure of an object's resistance to rotational motion, is affected by mass distribution. A larger moment of inertia means it will be harder to rotate the object.

5. How can you determine the stability of a rigid body?

The stability of a rigid body can be determined by analyzing its center of mass and its base of support. If the center of mass is above the base of support, the body is stable and less likely to tip over. However, if the center of mass falls outside the base of support, the body is unstable and may tip over. Additionally, the shape and distribution of the body's mass can also affect its stability.

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