How long will it take to come to rest?

  • Thread starter Max CR
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In summary, the steam engine is decelerating at 5.0 rad/s^2 and the goal is to find the time it takes for the engine to come to rest. Using the equation ωf = ωi + αt, the solution is to subtract the initial angular velocity from both sides and solve for t, which results in the time it takes for the engine to come to rest.
  • #1
Max CR
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Homework Statement



A steam engine is running at 200 RPM whe nits steam is shut off. The friction of its various parts produces torques that combine to decelerate the machine at 5.0 rad/s^2. How long will it take to come to rest?

Please help asap I have a test tomorrow.

Homework Equations





The Attempt at a Solution



th_7001.jpg
 
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  • #2
You are using the right equation. Note that the angular acceleration is negative, since the steam engine is coming to rest.
 
  • #3
THanks but how do I finish it??
 
  • #4
Solve for t. Are you having trouble with the algebra?
 
  • #5
0 rad/s / 25.94t = 0 and that is not right
 
  • #6
0 rad/s / 25.94t = 0 and that is not right

No, that won't work.

The equation initially is

ωf = ωi + αt

So you have come to the point where you have

0 = 20.94 - 5t

You want to get t on its own on one side of the equation. So the first step is to subtract 20.94 from both sides of the equation (whatever you do to one side you must also do it to the other side). When you do that, what do you get?
 
  • #7
THank you I got the answer now. I forgot that the 20.94 needs to go on the other side of the = in order to get t alone. THanks again
 
  • #8
:smile:You're welcome.
 

Related to How long will it take to come to rest?

1. How does an object come to rest?

An object comes to rest due to the forces acting upon it. When the net force on an object is zero, it will stop moving and come to rest.

2. What factors affect the time it takes for an object to come to rest?

The time it takes for an object to come to rest is affected by its mass, the force acting upon it, and the medium it is moving through. Objects with greater mass take longer to come to rest, while objects experiencing greater force or moving through a denser medium will come to rest more quickly.

3. Is there a universal formula to calculate the time it takes for an object to come to rest?

No, there is no universal formula as it depends on the specific circumstances of the object and the forces acting upon it. However, there are equations such as the Newton's Second Law of Motion that can be used to calculate the time it takes for an object to come to rest given certain parameters.

4. Can the time it takes for an object to come to rest be manipulated?

Yes, the time it takes for an object to come to rest can be manipulated by changing the forces acting upon it or altering its mass. For example, if the force acting upon an object is increased, it will come to rest more quickly.

5. How can we predict the time it will take for an object to come to rest?

We can predict the time it will take for an object to come to rest by using mathematical equations and principles such as Newton's Second Law of Motion. However, it is important to note that these predictions may not always be accurate as there can be other factors at play that can affect the time it takes for an object to come to rest.

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