Help me solve my dilema.Kinematics and dynamics of Rigid body problem.

In summary, the conversation discusses finding the acceleration-x ̈ of a load given a force and friction coefficient, and the mass of the body. Two approaches are mentioned, with the first being correct and the second incorrect. The first approach involves calculating work and setting it equal to the change in kinetic energy, while the second approach is not accurate due to friction taking away energy. The correct approach yields an acceleration of x=29/3g.
  • #1
CICCI_2011
23
0

Homework Statement



Find acceleration-x ̈ of the load. Force F=10G, friction μ=1/3, mass of he body is G.

I tried two ways of solving this problem but not sure if any is good. I think second is good. But wondering if first is also good?

Homework Equations



Ek=1/2 G/g x ̇^2

Fμ=G μ

The Attempt at a Solution



Please look at the picture.There you can see my effort in solving this problem. Thanks for any help.

http://s1198.photobucket.com/albums/aa453/nikola5210/?action=view&current=Load-Copy.png
 
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  • #2
I think you mean that the weight of the block is G, not the mass.

The first approach is correct, but not the second. It's not true that the rate at which work is being done is equal to the increase in kinetic energy, because friction takes away some of that energy.
 
  • #3
Work would be dA=Fdx-Gμdx

dA=10Gdx-G/3dx
dA=(10-1/3)Gdx
dA=29/3 Gdx

from which acceleration is x=29/3 g

For first approach I don't see how to get G μ+G/g x ̈ =F from Newton's second law?

Thanks for your help
 

Related to Help me solve my dilema.Kinematics and dynamics of Rigid body problem.

What is a rigid body?

A rigid body is a type of physical object that maintains its shape and size even when subjected to external forces. In other words, the distance between any two points on the object remains constant throughout its motion.

What is kinematics in relation to a rigid body?

Kinematics is the study of motion without considering the forces that cause the motion. In the context of a rigid body, kinematics focuses on the position, velocity, and acceleration of the body as it moves.

What is dynamics in relation to a rigid body?

Dynamics is the study of motion that takes into account the forces that cause the motion. In relation to a rigid body, dynamics involves analyzing how external forces affect the motion and stability of the body.

What are some common dilemmas encountered in solving kinematics and dynamics problems?

Some common dilemmas encountered in solving kinematics and dynamics problems include determining the correct equations to use, selecting the appropriate coordinate system, and properly interpreting the given information to set up the problem.

What are some strategies for solving kinematics and dynamics problems involving rigid bodies?

Some strategies for solving kinematics and dynamics problems involving rigid bodies include drawing a free body diagram, breaking the problem into smaller components, and using the principles of conservation of energy and momentum to simplify the calculations.

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