A man claims he can safely hold on to a 14.20 kg child in a head-on collision with a relative speed of 132. mi/h lasting for 0.100 s as long as he has his seat belt on.
(a) Find the magnitude of the average force needed to hold onto the child
convert 132 mi/hr to m/s
then divide by 0.100
To find the magnitude of the average force needed to hold onto the child, we can 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. The force, in this case, will be the force required to stop the child from moving during the collision.
First, we need to convert the mass of the child from kilograms to pounds since the relative speed is given in miles per hour.
1 kilogram (kg) is approximately equal to 2.20462 pounds (lbs).
So, the mass of the child is 14.20 kg x 2.20462 lbs/kg = 31.408844 lbs (approximately 31.4 lbs).
Next, we need to convert the relative speed from miles per hour to feet per second since the time is given in seconds.
1 mile per hour is approximately equal to 1.46667 feet per second.
So, the relative speed is 132 mi/h x 1.46667 ft/s = 193.33344 ft/s (approximately 193.3 ft/s).
Now, we can calculate the average force needed to hold onto the child using the formula:
Force = mass x acceleration
Since the time is very small (0.100 s), we can assume that the acceleration is constant during the collision. The acceleration can be calculated using the formula:
Acceleration = Change in velocity / Time
The change in velocity can be calculated as the final velocity (which is 0 since the child should come to a stop) minus the initial velocity (which is the relative speed).
Change in velocity = 0 ft/s - 193.33344 ft/s = -193.33344 ft/s
Acceleration = (-193.33344 ft/s) / 0.100 s = -1933.3344 ft/s^2
Now, we can substitute the values into the force formula:
Force = 31.408844 lbs x -1933.3344 ft/s^2
Simplifying the equation, we get:
Force ≈ -61,021.834 lbs * ft/s^2
The magnitude of the average force needed to hold onto the child is approximately 61,021.834 pounds multiplied by feet per second squared.