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
First, let's find the mass of the drop of blood.
Mass = 0.800 g = 0.0008 kg
(b) Now, we can find the force exerted by the blood vessel on the drop of blood using F = ma.
F = (0.0008 kg)(1.54 m/s²) = 0.001232 N
(c) When the arm is not swinging, the only force acting on the drop of blood is gravity. To find the force, we can use F = mg.
F = (0.0008 kg)(9.8 m/s²) = 0.00784 N
To solve part (b), you can use Newton's second law, which states that force (F) equals mass (m) multiplied by acceleration (a).
Given:
- Mass of the drop of blood (m) = 0.800 grams = 0.000800 kg (convert grams to kg)
- Acceleration (a) = 1.54 m/s^2 (as calculated in part a)
Using the formula F = ma, we can substitute the values:
F = (0.000800 kg) * (1.54 m/s^2)
F = 0.001232 N
Therefore, the force exerted by the blood vessel on the drop of blood at the bottom of the swing is approximately 0.001232 Newtons.
For part (c), if the arm were not swinging, the blood vessel would exert a force equal to the gravitational force acting on the drop of blood. The gravitational force is given by the formula F = mg, where g is the acceleration due to gravity, approximately 9.8 m/s^2.
Using the given mass (m) of 0.800 grams, we need to convert it to kilograms before calculating the force:
m = 0.000800 kg
Now, we can calculate the force exerted by the blood vessel if the arm were not swinging:
F = (0.000800 kg) * (9.8 m/s^2)
F = 0.00784 N
Therefore, if the arm were not swinging, the blood vessel would exert a force of approximately 0.00784 Newtons on the drop of blood.
To solve part (b) of the problem, you can use the equation F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the mass is given as 0.800 grams, which needs to be converted to kilograms by dividing by 1000.
The acceleration can be calculated using the formula a = v^2 / r, where v is the velocity and r is the radius or length of the arm. We can find v by dividing the angular displacement (45°) by the time taken (0.530 s) to get the angular velocity, and then multiplying it by the radius.
The formula for the angular velocity is ω = θ / t, where ω is the angular velocity, θ is the angular displacement, and t is the time taken. In this case, the angular displacement is 45° (which needs to be converted to radians), and the time taken is 0.530 s.
Once you have the velocity, you can substitute it into the formula for acceleration and then calculate the force using F = ma.
Now, for part (c), if the arm were not swinging, it means that there would be no angular displacement and hence no angular velocity. Therefore, the acceleration would be zero, resulting in no force required to maintain the blood drop in the fingertips.
I hope this explanation helps you solve parts (b) and (c) of the problem.