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Gostronge · Jun 24, 2007, 07:38 PM

Two dogs and a cat fight over a 1kg beef bone. The bone accelerates to the right at 2.5m/s^2 Dog A pulls to the left with a force of 300N and Dog B pulls to the roght a force of 375N

What force does the Cat exert on the bone?

Capuchin · Jun 24, 2007, 11:38 PM

You're going to have to draw a diagram because I have no idea what "right" means, or where the cat is.

ebaines · Jun 25, 2007, 01:52 PM

I assume you know the famous F=ma equation, right? Well, here you know the bone's mass and acceleration, so you can calculate what the sum of all the forces must be, and its direction. Remember that forces are vectors, so they have a direction, and in adding forces you add forces that are going in the positive direction and subtract forces going in the negative direction. For this problem let's call the direction to the right positive, and the left is negative. Now, the total force must be going to the right, since that's the direction the bone accelerates. Call that total force $\vec {F _{Total}}$ . Once you have that calculated, you can find the force the cat exerts by subtracting the forces that the two dogs exert from $\vec {F _{Total}$ :

$<br /> \vec {F _{Cat}} = \vec {F _{Total}} - \vec {F _{Dog A}} - \vec {F _{Dog B}} <br />$

Hope this helps.

Gostronge · Jun 25, 2007, 07:13 PM

Originally Posted by ebaines

I assume you know the famous F=ma equation, right? Well, here you know the bone's mass and acceleration, so you can calculate what the sum of all the forces must be, and its direction. Remember that forces are vectors, so they have a direction, and in adding forces you add forces that are going in the positive direction and subtract forces going in the negative direction. For this problem let's call the direction to the right positive, and the left is negative. Now, the total force must be going to the right, since that's the direction the bone accelerates. Call that total force $\vec {F _{Total}}$ . Once you have that calculated, you can find the force the cat exerts by subtracting the forces that the two dogs exert from $\vec {F _{Total}$ :

$<br /> \vec {F _{Cat}} = \vec {F _{Total}} - \vec {F _{Dog A}} - \vec {F _{Dog B}} <br />$

Hope this helps.

The force of the Cat equels 2.5N (F=ma). If I add Dog A, Dog B and the Cat's force which will give me the totel force, right? But by using the total force to subtract Dog A and B will only give me what I calculated at the beginning, the Cat at 2.5N.

what I have tried doing is Dog B - Dog A = force to the right and adding the Cat's force at 2.5N to the right, which gives me a answer of 77.5N to the right. Because this question is a multiple choice I'm still confuse on picking the following answers. I think it C but have a feeling that it might be A as well.

a 72.5N right
b 77.5N left
c 77.5 right
d 72.5 left

ebaines · Jun 26, 2007, 10:17 AM

I think what you mean is that the Total Force is 2.5N. That's the force that would have to be exerted on a 1 Kg bone to accelerate it at 2.5 m/s^2. Do you see that?

You know that Dog A is pulling to the left at 300N and Dog B is pulling to the right at 375N, so the total of these two forces is 75N to the right. Do you see how that works? Now you need to determine what additional force, and in what direction, is applied by the cat so that you get a total force for the two dogs plus the cat to be 2.5N to the right. The sum of the forces of the two dogs alone is too much to the right, so clearly the cat must be pulling left - can you determine by what amount?