One study suggests that a brain concussion can occur if a person's head is subjected to an acceleration as small as 60g, where g is the acceleration of gravity.
a. If the mass of the person's head is 4.5 kg, what is the magnitude of the force?
(Express your answer to two significant figures and include appropriate units.)
b. If the impulse delivered to the person's head is 19 kg⋅m/s, over what time interval is the force applied?
(Express your answer to two significant figures and include appropriate units.)
60 g is not a small force.
a. F=ma
Force=4.5*60*9.8 N
b. Force*time=19
time= 19/aboveForce
To solve this problem, we can use the formulas relating force, mass, acceleration, and impulse.
a. To find the magnitude of the force, we need to calculate the acceleration first. The formula for acceleration is:
acceleration = force/mass
We are given the acceleration (60g), and we know the mass of the person's head (4.5 kg). We can rearrange the formula to solve for force:
force = acceleration * mass
Let's substitute the given values into the formula:
force = (60g) * (4.5 kg)
Now we need to convert g to meters per second squared (m/s²) since it is given in terms of the acceleration due to gravity. We know that 1 g is approximately equal to 9.8 m/s². So, we can calculate the force as follows:
force = (60 * 9.8 m/s²) * (4.5 kg)
Calculate the product:
force = 2940 N * 4.5 kg
force ≈ 13230 N
Therefore, the magnitude of the force is approximately 13230 N.
b. To find the time interval for which the force is applied, we can use the formula for impulse:
impulse = force * time
We are given the impulse (19 kg⋅m/s), and we need to solve for time. Rearranging the formula gives us:
time = impulse / force
Let's substitute the given values into the formula:
time = 19 kg⋅m/s / 13230 N
Calculating the division:
time ≈ 0.0014 s
Therefore, the time interval for which the force is applied is approximately 0.0014 seconds.