Dynamics Question (Kinetics& energy)

In summary, the problem involves two blocks connected by a light inextensible cord and small massless pulleys. The goal is to determine the speed of block B when it returns to the equilibrium position after being pulled down 500 mm and released from rest. The equation used is T1 + U1 = T2 + U2 and the attempt at a solution involves considering the potential and kinetic energy of the system. However, the attempt at a solution overlooks the fact that the spring is already stretched in the equilibrium position, resulting in a negative value for the equation. The correct answer is 2.16 m/s.
  • #1
gomerpyle
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Homework Statement



The two blocks are connected by a light inextensible cord, which passes around small

massless pulleys as shown below. If block B is pulled down 500 mm from the equilibrium

position and released from rest, determine its speed when it returns to the equilibrium

position.

http://s3.amazonaws.com/answer-board-image/201069134736341168802377387504353.gif


Homework Equations



T1 + U1 = T2 + U2

The Attempt at a Solution



If it's pulled down below equilibrium and held there, then T1 of the system is zero because both blocks are not moving. At the moment B passes through the equilibrium, there is no more potential energy, only kinetic, then the equation would look like:

U1 = T2

The problem I'm running into is that I get a negative value for the left side of this equation, which is impossible because then it would have to go under a square root when solving for the velocity.

for U1 I had:

mgha - mghb + 0.5kx^2

Since 'b' moves down 0.5m, a moves up 0.25 and the spring is stretched 0.25. Is this right since A is attached to the pulley and B is simply hanging? If that's the case then:

(2)(9.81)(0.25) - (10)(9.81)(0.5) + 0.5(800)(0.25)^2

Which is negative. Supposedly the answer is 2.16 m/s.
 
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  • #2
You neglected the fact that the spring is already stretched in the equilibrium position before the block B is pulled down.
 

FAQ: Dynamics Question (Kinetics& energy)

What is the difference between kinetics and energy in dynamics?

Kinetics is the study of motion and its causes, while energy is the ability to do work. In dynamics, kinetics deals with the forces that cause motion, while energy deals with the work that is done by those forces.

How are kinetics and energy related?

Kinetics and energy are closely related in dynamics because forces cause motion, and motion involves energy. Kinetic energy is the energy of motion, and potential energy is the energy that an object has due to its position or state.

What is the difference between potential and kinetic energy?

Potential energy is stored energy that an object has due to its position or state, while kinetic energy is the energy of motion. Potential energy can be converted into kinetic energy and vice versa.

How does energy conservation apply to dynamics?

Energy conservation states that energy cannot be created or destroyed, only transferred or converted from one form to another. In dynamics, this means that the total amount of energy in a system remains constant, even if it changes form or location.

What is the role of energy in determining the behavior of objects in motion?

Energy plays a crucial role in determining the behavior of objects in motion. The amount of kinetic energy an object has is related to its speed and mass, while potential energy is related to its position or state. These energy factors affect an object's velocity, acceleration, and overall motion.

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