Hi, help me to check my answers, dynamics, energy and work

In summary, the problem involves finding the final speed of a second box (mass = 1kg) on a rough ramp inclined at 60° with respect to the x axis, when the first box (mass = 5 kg) has descended a distance of 0.6 meters. The system is released from its stationary state and includes a compressed spring (length x = 0.2 meters) and ideal rope, spring, and pulley (no mass, no elongation or contraction). The dynamic friction coefficient is 0.2 and the spring's elasticity constant is 200 Newtons/meters. The solution involves using free-body diagrams and energy balances to find the acceleration and then using cinematic equations to find the speed. Additional
  • #1
Eduardo Leon
6
0

Homework Statement


Whats is the final speed of the second box(mass = 1kg) when the first one (mass = 5 kg) has descended a distance equal to 0.6 meters in the rough ramp inclined 60° respect the x axis. Consider the spring is compressed a length x = 0.2 meters. The second box is tied to the spring and the system is released from its stationary state. For this case, consider the rope, the spring and the pulley are ideal (have no mass and the rope doesn't get elonged or contracted), the dynamic friction coefficent is 0.2, and the elasticity constant of the spring k=200 Newtons/meters?
  • Second box(mass = 1kg)
  • First box(mass = 5 kg)
  • Distance descended to 0.6 meters (rough ramp inclined 60° respect the x axis)
  • The spring is compressed a length x = 0.2 meters.
  • The rope, the spring and the pulley are ideal (have no mass and the rope doesn't get elonged or contracted).
  • Dynamic friction coefficent is 0.2
  • Elasticity constant of the spring k=200 Newtons/meters

    It's the 27th excersice
    37687315_10217176949561992_6753722960701292544_n.jpg

Homework Equations


  • Free-body diagrams
  • Work (W=Fxd)
  • Mechanic Energy Balance (conservative and non conservative system)
  • Cinematic equation for final speed V^2Final = V^2initial +2 a(Xfinal - Xinitial)
Being
V^2Final the square power of the speed at a t time
V^2initial the square power of the speed at a initial time
a the acceleration
(Xfinal the displacement at a the t time
Xinitial the displacement at a the initial time

The Attempt at a Solution


The speed I calculated is equal to 3.68 m/s
The acceleration of the system when released (thanks to the free-body diagrams) = 11,29m/s^2

In order to find the speed of the second box, I first found the height where it will arrive after the spring releases, using energy balances. Then, after findig the acceleration via Free-body diagram used cinematic equations for speed according to de enunciated distance.
 

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    37687315_10217176949561992_6753722960701292544_n.jpg
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  • #2
I bet that this has an accompanying figure. Look at it from our point of view. Without the figure, do you think the problem and scenario is clear based just on what you have written?

Zz.
 
  • #3
ZapperZ said:
I bet that this has an accompanying figure. Look at it from our point of view. Without the figure, do you think the problem and scenario is clear based just on what you have written?

Zz.
Done.
 
  • #4
Eduardo Leon said:

Homework Statement


Whats is the final speed of the second box(mass = 1kg) when the first one (mass = 5 kg) has descended a distance equal to 0.6 meters in the rough ramp inclined 60° respect the x axis. Consider the spring is compressed a length x = 0.2 meters. The second box is tied to the spring and the system is released from its stationary state. For this case, consider the rope, the spring and the pulley are ideal (have no mass and the rope doesn't get elonged or contracted), the dynamic friction coefficent is 0.2, and the elasticity constant of the spring k=200 Newtons/meters?
  • Second box(mass = 1kg)
  • First box(mass = 5 kg)
  • Distance descended to 0.6 meters (rough ramp inclined 60° respect the x axis)
  • The spring is compressed a length x = 0.2 meters.
  • The rope, the spring and the pulley are ideal (have no mass and the rope doesn't get elonged or contracted).
  • Dynamic friction coefficent is 0.2
  • Elasticity constant of the spring k=200 Newtons/meters

    It's the 27th excersice
    View attachment 228331

Homework Equations


  • Free-body diagrams
  • Work (W=Fxd)
  • Mechanic Energy Balance (conservative and non conservative system)
  • Cinematic equation for final speed V^2Final = V^2initial +2 a(Xfinal - Xinitial)
Being
V^2Final the square power of the speed at a t time
V^2initial the square power of the speed at a initial time
a the acceleration
(Xfinal the displacement at a the t time
Xinitial the displacement at a the initial time

The Attempt at a Solution


The speed I calculated is equal to 3.68 m/s
The acceleration of the system when released (thanks to the free-body diagrams) = 11,29m/s^2

In order to find the speed of the second box, I first found the height where it will arrive after the spring releases, using energy balances. Then, after findig the acceleration via Free-body diagram used cinematic equations for speed according to de enunciated distance.
Maybe I am making some silly error, but it seems to me the box will not descend that far.
Some of the details (in English) are not entirely clear. Is the spring already compressed by 0.2m before the system is released? Is the 0.6m descent vertical discplacement or parallel to the plane (I assumed it parallel to the plane, leading to total spring compression 0.8m).
Very rough analysis: GPE lost by 5kg mass < 5g(0.6)0.87<26J.
Work done on spring =½200(0.82-0.22)=60J

Please either correct my assumptions or post detailed working (preferably both).
 
  • #5
haruspex said:
Maybe I am making some silly error, but it seems to me the box will not descend that far.
Some of the details (in English) are not entirely clear. Is the spring already compressed by 0.2m before the system is released? Is the 0.6m descent vertical discplacement or parallel to the plane (I assumed it parallel to the plane, leading to total spring compression 0.8m).
Very rough analysis: GPE lost by 5kg mass < 5g(0.6)0.87<26J.
Work done on spring =½200(0.82-0.22)=60J

Please either correct my assumptions or post detailed working (preferably both).

The sexond box is compressing the spring before the system is released.

The first box descends o,6 meters parallel to the plane.

But the descending of the first box (the left one) means the rising of the second one (the one tied directly to the spring).
 
  • #6
Eduardo Leon said:
The sexond box is compressing the spring before the system is released.

The first box descends o,6 meters parallel to the plane.

But the descending of the first box (the left one) means the rising of the second one (the one tied directly to the spring).
Doh! I transcribed the diagram wrongly!
Makes sense now, but I get a rather smaller number. Please post your working.
 
  • #7
haruspex said:
Doh! I transcribed the diagram wrongly!
Makes sense now, but I get a rather smaller number. Please post your working.

I redid it. Now what I've done is calculate what heigt the 2nd box will reach (gave equals to 0.15 meters (the height obtained was the same using 2 different reference systems).

Then calculated de acceleration of the system via free-body diagrams (Acceleration= 11,29m/s^2)

And finally decomposed the 0,6 meters of the ramp to find the y component (height) to know that the second box raises 0,52 meters when the system moves

Then used cinematic equations to calculate the final speed when the box raised (final speed= 2,89m/s)
 
Last edited:
  • #8
Eduardo Leon said:
what heigt the 2nd box will reach (gave equals to 0.15 meters
If it only rises 0.15m there is no way way the other box will move 0.6m.
Eduardo Leon said:
calculated de acceleration
Since we do not care about time, acceleration is uninteresting. You can do it all by energy.

I still get a smaller value for the speed. Please post your working!
 
  • #9
Eduardo Leon said:
I redid it. Now what I've done is calculate what heigt the 2nd box will reach (gave equals to 0.15 meters

Then calculated de acceleration of the system via free-body diagrams (Acceleration= 11,29m/s^2)

And finally decomposed the 0,6 meters of the ramp to find the y component (height) to know that the second box raises 0,52 meters when the system moves

Then used cinematic equations to calculate the final speed when the box raised (final speed= 2,89m/s)
haruspex said:
If it only rises 0.15m there is no way way the other box will move 0.6m.

Since we do not care about time, acceleration is uninteresting. You can do it all by energy.

I still get a smaller value for the speed. Please post your working!
I mean, the 0,15 meters is what the 2nd box raises by the action of the spring and the 0.52 is what the 2nd box raises by releasing the system. other value for velocity I calculated by making an energy balance from the height -0,2m (before releasing the system to the higest ponit the second box will reach is 0.89 m/s but I'm not sure about that result).
 
  • #10
Eduardo Leon said:
I mean, the 0,15 meters is what the 2nd box raises by the action of the spring and the 0.52 is what the 2nd box raises by releasing the system. other value for velocity I calculated by making an energy balance from the height -0,2m (before releasing the system to the higest ponit the second box will reach is 0.89 m/s but I'm not sure about that result).
If you just keep describing your method I cannot figure out where we diverge. Please post all the steps.
 

Related to Hi, help me to check my answers, dynamics, energy and work

1. What is dynamics?

Dynamics is the branch of physics that studies the motion of objects and the forces that cause this motion.

2. What is energy?

Energy is the ability of an object or system to do work. It exists in many forms such as kinetic, potential, thermal, chemical, and nuclear energy.

3. What is work?

Work is defined as the force applied to an object multiplied by the distance the object moves in the direction of the force. It is a measure of the energy transferred to or from an object.

4. How are dynamics, energy, and work related?

Dynamics, energy, and work are closely related as they all deal with the movement and forces acting on objects. Dynamics describes the motion of objects, energy is the ability to do work, and work is the transfer of energy from one object to another.

5. How can I check my answers for dynamics, energy, and work problems?

To check your answers for problems involving dynamics, energy, and work, you can use equations and formulas specific to each concept, and ensure that your units and calculations are correct. It is also helpful to double check your work and use real-world examples to verify your answers.

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