How Do You Solve a Relative Velocities Problem with Missing Equations?

In summary, the problem involves finding the relative velocities of two objects, but there are only two equations and three unknowns. The attempt at a solution involves using the cable constraint equation or energy conservation, but it is unclear which approach is correct. Further guidance is needed to find a third equation.
  • #1
coltin.walsh
7
0
Dynamics Help Needed! Relative velocities problem

Homework Statement



see link:

http://www.flickr.com/photos/55153239@N03/6199846646/


Homework Equations



Can you please help me solve this problem?
I have 3 unknowns: Va, Vb, and Thetha; but only two equations

Vb(cos(theta)) - Va(cos30) = 5.6cos70
Vb(sin(theta)) - Va(sin30) = 5.6sin70

I need a third equation?


The Attempt at a Solution



To get the two above equations, I took into account:

Vb/a = Vb - Va

Then I broke each vector into components. I end up with the two above equations. But I don't know where to go from here. I need a third equation either relating theta to Va or Vb, or a cable constraint equation, etc. I need some help.
 
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  • #2


Is it right to use the cable constraint equation of: 2Xa+3Xb=constant.
then taking the derivative to get: 2Va+3Vb=0? Or is that not correct?
 
  • #3


How about energy conservation?

(I haven't done this problem, so this is truly just a suggestion, but I think it would lead to your answer).
 

FAQ: How Do You Solve a Relative Velocities Problem with Missing Equations?

What is the definition of relative velocity?

Relative velocity is the velocity of an object in relation to another object. It is the difference between the velocities of the two objects and takes into account their direction of motion.

How do I calculate relative velocity in a dynamics problem?

To calculate relative velocity, you need to find the difference between the velocities of the two objects in the problem. This can be done by subtracting the two velocities, taking into account their direction of motion.

What is the importance of understanding relative velocities in dynamics?

Understanding relative velocities is important in dynamics because it allows us to accurately predict the motion of objects in relation to each other. It also helps in analyzing collisions and other interactions between objects.

Can you give an example of a dynamics problem involving relative velocities?

Sure, let's say two cars are traveling towards each other on a straight road. Car A has a velocity of 60 km/h and car B has a velocity of 40 km/h. The relative velocity of car A with respect to car B would be 20 km/h (60 km/h - 40 km/h).

How does the concept of relative velocity apply to rotational motion?

In rotational motion, relative velocity is the difference between the angular velocities of two rotating objects. It takes into account the direction of rotation and can be used to analyze the interactions between rotating objects.

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