Need Help With Calculating Forces (Circular Motion)

[kgianqu2]

While a person is walking, his arms (with typical lengths 70 cm measured from the shoulder joint) swing through approximately a 45 degree angle in 0.5 s. As a reasonable approximation, we can assume that the arm moves with constant speed during each swing.
Find the magnitude of the force that the blood vessel must exert on the drop of blood.

(I've already calculated the acceleration of 1.00 g drop of blood to be 1.7m/s^2.)

I've tried using n-w = m(v^2/r). Its not going so well. Is this the correct equation? Can you get me started? Thank you.

 

[deep838]

could you explain what you mean by drop of blood?

 

[kgianqu2]

That's all that the problem gives. I assume it just means one drop of blood that is in the arm.

Also I need to find: What force would the blood vessel exert if the arm were not swinging?

 

[deep838]

we can assume that the arm moves with constant speed during each swing.

How is that even possible? I mean in that case, the arm would move in a cycle! That's not how a man/woman usually walk... It's more like a harmonic motion, getting max when the angle is 0° and minimum when it's 90°! Did you think about that?

:P Sorry for the late reply!

 

[Nickie]

Hello,

Thank you for reaching out for help with calculating forces in circular motion. I would first like to commend you for attempting to use the correct equation and for providing the necessary information for the problem.

From your given information, we know that the arm is swinging with a constant speed and a 45 degree angle in 0.5 seconds. This means that the arm is undergoing uniform circular motion, where the speed and radius remain constant. In this case, the correct equation to use is indeed the one you mentioned: F = mv^2/r.

To get started, we will need to find the mass of the blood drop. This can be calculated by using the density of blood (approximately 1060 kg/m^3) and the volume of a spherical drop (4/3πr^3). Once we have the mass, we can plug it into the equation along with the given acceleration of 1.7m/s^2 and the length of the arm (0.7m) to solve for the force exerted by the blood vessel.

I would also like to note that in this situation, we are assuming that the force exerted by the blood vessel is equal to the centripetal force needed to keep the blood drop moving in a circular path. This may not be entirely accurate as there may be other forces acting on the blood drop, such as air resistance. However, as a reasonable approximation, the equation we are using should give us a good estimate of the force.

I hope this helps to get you started on solving the problem. If you are still having trouble, I would recommend checking your calculations and units to ensure they are correct. You can also refer to your textbook or consult with a classmate or teacher for further assistance. Keep up the good work in your scientific studies!