While a person is walking, his arms swing through approximately a 45° angle in .530s. As a reasonable approximation, we can assume that the arm moves with constant speed during each swing. A typical arm is 70.0 cm long, measured from the shoulder joint. (a) What is the acceleration of a .800 gram drop of blood in the fingertips at the bottom of the swing?
1.54m/s^s i got correct
(b) Find the force that the blood vessel must exert on the drop of blood in part a.
im having touble solving this problem and part c
(c) What force would the blood vessel exert if the arm were not swinging?
i know the formula i use is F=ma
I am having trouble with part b myself but for part c the only force is gravity. So F=ma =.0008kg*9.8m/s^2 =0.00784N
Ah, the wonders of blood vessel physics! Let's tackle these questions one swing at a time!
(a) So, you already found the correct acceleration of the drop of blood to be 1.54 m/s^2. Well done! Keep that number handy for the next steps.
(b) To find the force that the blood vessel must exert on the drop of blood, we can indeed use the formula F = ma. However, we need to consider the acceleration as a centripetal acceleration because it's the result of circular motion.
The centripetal acceleration is given by the formula a = ω^2r, where ω is the angular velocity and r is the radius (length of the arm). We don't have the angular velocity, but we know that each swing takes 0.530 seconds and covers a 45° angle.
To find ω, we can use the formula ω = θ/t, where θ is the angle and t is the time taken. Convert the angle to radians first (45° = 45π/180), and then calculate ω (angular velocity).
Once you have the angular velocity, you can substitute it into the formula a = ω^2r to find the centripetal acceleration. And finally, use F = ma with the calculated acceleration to determine the force.
(c) Now, let's consider the arm not swinging. In this case, the acceleration is zero because there is no circular motion (remember Newton's first law?). So, if the acceleration is zero, the force required would also be zero. We can say the blood vessel doesn't need to push against the blood drop when the arm isn't swinging.
Keep up the good work, and remember, laughter is always a great way to relax your blood vessels!
To solve part b, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration.
We are given the mass of the drop of blood, which is 0.800 grams. We have already calculated the acceleration in part a, which is 1.54 m/s^2. However, we need to convert the mass from grams to kilograms, as the SI unit for mass is kilograms.
1 gram = 0.001 kilograms
So, the mass of the drop of blood is 0.800 grams x (0.001 kilograms/1 gram) = 0.0008 kilograms.
Substituting the values into the formula F = ma:
F = (0.0008 kilograms)(1.54 m/s^2) = 0.001232 Newtons
Therefore, the force that the blood vessel must exert on the drop of blood at the bottom of the swing is approximately 0.001232 Newtons.
To solve part c, we need to consider the force exerted when the arm is not swinging. In this case, the arm is stationary or moving with constant velocity, indicating zero acceleration (a = 0).
Using the formula F = ma, when a = 0, the force (F) will also be zero. Therefore, the blood vessel would exert zero force on the drop of blood if the arm were not swinging.
To solve part (b) of the problem, you will need to use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this case, you have already calculated the acceleration of the blood drop in part (a) as 1.54 m/s^2. Now, you need to find the force that the blood vessel must exert on the drop of blood.
The mass of the blood drop is given as 0.800 grams. However, it is important to convert the mass to kilograms since the SI unit of force is Newtons (N), which is kg·m/s^2. So, the mass of the blood drop is 0.800 grams = 0.800 * 10^-3 kg = 0.0008 kg.
Now you can substitute the values into the formula:
F = ma
F = (0.0008 kg) * (1.54 m/s^2)
F ≈ 0.0012 N
Therefore, the force that the blood vessel must exert on the drop of blood is approximately 0.0012 Newtons.
To solve part (c), you need to consider the scenario where the arm is not swinging, which means there is no acceleration acting on the blood drop. In this case, the acceleration is zero (a = 0).
Using the same formula, F = ma, and substituting the values:
F = (0.0008 kg) * (0 m/s^2)
F = 0
Therefore, the force that the blood vessel would exert if the arm were not swinging is zero. In other words, when there is no acceleration, there is no force required to maintain the blood drop in its position.