Mechanics/Kinetics of Particles

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In summary, the conversation discusses a problem involving two weights hanging from a rope through two pulleys. The weight of each object is given and one has an initial speed. The conversation then goes into a detailed explanation of how to solve the problem, with emphasis on the conversion of potential energy to kinetic energy. After much discussion and attempts, an error is discovered in the calculation of kinetic energy. Once this error is corrected, the problem is successfully solved.
  • #1
scluggy
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Two weights are hanging from a rope that goes through two pulleys as shown below:

_______
| O
| / \
| | |
\ / |
O |
| |
A B

A weighs 3 kg
B weighs 2 kg

B has an initial speed of 0.8 m/s

How far will B drop before A reaches a speed of 0,6 m/s?

The mass of the pulley and the cable can be neglected.

I have been trying to resolve this for some time now but will always get the wrong answer. The way I believe it should work is:

The potential energy + the kinetic energy for the system is the same at the start and end of this so we would have a conversion of energy from potential energy to kinetic energy. So I have set it up as having 0 potential energy to start off with (height = 0)

mgh = 2*9.81*0 = 0 and 3*9.81*0 = 0

The velocity for B would be twice that of the velocity for A due to the pulley system.

The initial kinetic energy would be:
0.5mv^2 = 0.5*2*0.8^2 and 0.5*3*-0.4^2

So the whole amount of energy for this would be
0.64-0.24 = 0.4

If we then set this equal to the same formula but for the A speed of 0.6 m/s we get
0.88 = (kinetic energy A) + (kineric energy B) + (potential energy A) + (potential energy B)

0.4 = 0.5*3*-0.6^2 + 0.5*2*1.2^2 + 3*9.81*h/2 + 2*9.81*h

Which makes h = - 100 / 6867

This is incorrect as the answer should be 0.224

Can someone see where I am going wrong and perhaps help with how this should be resolved? I have been trying to resolve this issue for some time now with different methods but will always come up with the wrong answer.

Thankful for any suggestions!
 
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  • #2
scluggy said:
The velocity for B would be twice that of the velocity for A due to the pulley system.

The initial kinetic energy would be:
0.5mv^2 = 0.5*2*0.8^2 and 0.5*3*-0.4^2

So the whole amount of energy for this would be
0.64-0.24 = 0.4
Your error is in having a negative kinetic energy! The KE of mass B is positive, not negative.

Regardless of your sign convention, the speed is squared so the KE is always positive. (To maintain sanity, I would choose a sign convention of up = +, down = -.)
 
  • #3
Thank you so much! I was really struggling with this problem but now it's solved thanks to your help :smile:
 

FAQ: Mechanics/Kinetics of Particles

What is the difference between mechanics and kinetics?

Mechanics is the study of motion and forces acting on objects, while kinetics is the study of the causes of motion and the forces that cause it.

How do you calculate the velocity of a moving particle?

The velocity of a particle can be calculated by dividing the change in displacement by the change in time. This is also known as the average velocity.

What is the relationship between mass and acceleration?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be expressed as a = F/m.

What is the difference between linear and angular momentum?

Linear momentum refers to the quantity of motion in a straight line, while angular momentum refers to the quantity of motion in a rotational direction. Linear momentum is calculated as mass multiplied by velocity, while angular momentum is calculated as moment of inertia multiplied by angular velocity.

What is the law of conservation of momentum?

The law of conservation of momentum states that the total momentum of a closed system remains constant, meaning that the total initial momentum of a system before a collision is equal to the total final momentum after the collision. This law is based on the principle of conservation of energy and is a fundamental concept in mechanics and kinetics.

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