A man claims he can safely hold on to a 9.7-kg child in a head-on collision with a relative speed of 112-mi/h lasting for 0.12 s as long as he has his seat belt on.
(a) Find the magnitude of the average force needed to hold onto the child. HELP
The child is going from a speed of 112 mi/h to a speed of 0 in .12 seconds...so their is a deceleration...Does this help?
112 m/h = 180 km/h = 50 m/s
The deceleration rate is
a = (50 m/s)/0.12s = 416 m/s^2
That's about 42 g's.
The force to hold the child required is F = m a, which is about 42 times the child's weight.
Do the calculation and answer in Newtons or pounds..
N=m*v/t
To find the magnitude of the average force needed to hold onto the child in a head-on collision, we can use Newton's second law of motion, which states:
Force = mass × acceleration
First, we need to convert the relative speed from miles per hour to meters per second because the units need to be in the SI system. We know that 1 mile is approximately equal to 1.609 kilometers, and 1 kilometer is equal to 1000 meters. Therefore, to convert mi/h to m/s, we can use the following conversion factor:
1 mi/h ≈ 1.609 × 1000 ÷ 3600 m/s
So, the relative speed is:
112 mi/h ≈ 112 × 1.609 × 1000 ÷ 3600 m/s
Next, we can find the acceleration by dividing the change in velocity by the time duration of the collision. The change in velocity during the collision can be calculated by multiplying the relative speed by 2:
Change in velocity = 2 × relative speed
Now, let's find the change in velocity:
Change in velocity = 2 × (112 × 1.609 × 1000 ÷ 3600) m/s
Now, we have all the necessary information to find the magnitude of the average force using Newton's second law. Rearranging the equation, we get:
Force = mass × acceleration
The mass of the child is given as 9.7 kg, and the acceleration is the change in velocity divided by the duration of the collision (0.12 s):
Force = 9.7 kg × (2 × (112 × 1.609 × 1000 ÷ 3600) m/s) ÷ 0.12 s
Now, we can calculate the magnitude of the average force needed to hold onto the child by plugging the values into the equation.