A car is traveling at 60.0 mph when
it collides with a stone wall. The car
comes to rest after the first foot of
the car is crushed. What was the
average horizontal force acting on a
150-lb driver while the car came to
rest? If five cardboard boxes, each 4
ft wide and filled with sand had been
placed in front of the wall, and the
car moved through all that sand
before coming to rest, what would
the average force acting on the driver
have been then?
no answer
To answer the first part of your question, we need to calculate the average horizontal force acting on the driver while the car comes to rest. Let's break down the problem step by step:
Step 1: Convert the speed of the car from miles per hour (mph) to feet per second (ft/s).
1 mile = 5280 feet, 1 hour = 3600 seconds.
So, 60 mph = (60 * 5280) / 3600 = 88 ft/s.
Step 2: Calculate the initial kinetic energy of the car.
The formula for kinetic energy is: KE = 0.5 * mass * velocity^2.
The mass of the car is not given, but we are given that the driver in the car weighs 150 lbs. We need to convert this to mass in the correct unit system.
1 lb = 0.453592 kg.
So, the mass of the driver is: 150 lbs * 0.453592 kg/lb = 68.0392 kg.
The initial kinetic energy of the car is: KE = 0.5 * 68.0392 kg * (88 ft/s)^2.
Step 3: Calculate the final kinetic energy of the car.
Since the car comes to rest after the first foot of the car is crushed, the final velocity is 0 ft/s. Therefore, the final kinetic energy is also 0.
Step 4: Calculate the work done on the car to bring it to rest.
The work done can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy. So, W = ΔKE.
W = Final KE - Initial KE = 0 - (0.5 * 68.0392 kg * (88 ft/s)^2).
Step 5: Calculate the average force acting on the driver.
The average force can be calculated using the formula: average force = work done / distance.
Given that the distance is 1 foot, we have: average force = (0.5 * 68.0392 kg * (88 ft/s)^2) / 1 ft.
Now, let's move on to the second part of your question. If five cardboard boxes, each 4 ft wide and filled with sand, were placed in front of the wall and the car moved through all that sand before coming to rest, we need to calculate the average force acting on the driver in this scenario.
Step 1: Calculate the total distance traveled by the car.
Since the car moved through all the sand-filled boxes, the distance traveled by the car will be the sum of the widths of all the boxes. So, total distance = 5 boxes * 4 ft/box = 20 ft.
Step 2: Calculate the average force on the driver.
Using the same formula as before, average force = work done / distance.
Given that the distance is 20 ft, we have: average force = (0.5 * 68.0392 kg * (88 ft/s)^2) / 20 ft.
Now you have the formulas and steps to calculate the average horizontal force acting on the driver in both scenarios. Simply plug in the values and calculate the results.