A 75 kg passenger in a van is wearing a seat belt whent he van moving at 15m/s, collides with a conrete wall. The front end of the van collapses 0.50 m as it comes to rest.
a) what was the paseenger's kinetic energy before the crash
b) What average force did the seat belt exert on the passengfer during the crash?
KE= 1/2 mv^2
Force*distance= 1/2 mv^2 solve for force
To find the answers to these questions, we can use the principles of conservation of energy and the work-energy theorem.
a) To determine the passenger's kinetic energy before the crash, we can use the equation:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Given:
Mass (m) = 75 kg
Velocity (v) = 15 m/s
Using the formula, we can calculate the passenger's kinetic energy:
KE = (1/2) * 75 kg * (15 m/s)^2
KE = 8437.5 Joules
So, the passenger's kinetic energy before the crash is 8437.5 Joules.
b) To find the average force exerted by the seat belt on the passenger during the crash, we can use the equation:
Work (W) = force * distance
Since the work done on an object is equal to the change in its kinetic energy, we can set up the following equation:
Force * distance = change in kinetic energy
Given:
Distance (d) = 0.50 m
Change in kinetic energy = Initial kinetic energy (before crash) - Final kinetic energy (after crash)
Change in kinetic energy = 8437.5 J - 0 J (since the van comes to rest)
Substituting the values, the equation becomes:
Force * 0.50 m = 8437.5 J
We can solve for force:
Force = 8437.5 J / 0.50 m
Force = 16875 N
Therefore, the average force exerted by the seat belt on the passenger during the crash is 16875 Newtons.
To solve this problem, we need to use the concepts of kinetic energy and work.
a) The passenger's kinetic energy before the crash can be calculated using the formula:
Kinetic energy = 0.5 * mass * velocity^2
Given:
Mass (m) = 75 kg
Velocity (v) = 15 m/s
Plugging these values into the formula:
Kinetic energy = 0.5 * 75 kg * (15 m/s)^2
To calculate, firstly, square the velocity:
(15 m/s)^2 = 225 m^2/s^2
Then, multiply the mass by the squared velocity:
Kinetic energy = 0.5 * 75 kg * 225 m^2/s^2
Evaluating the expression:
Kinetic energy = 8437.5 J (Joules)
Therefore, the passenger's kinetic energy before the crash was 8437.5 Joules.
b) To find the average force exerted by the seat belt on the passenger during the crash, we need to determine the work done by the seat belt.
The work done is given by the formula:
Work = Force * Distance
Given:
Distance (d) = 0.50 m
The work done by the seat belt is equal to the change in kinetic energy:
Work = Change in kinetic energy = Final kinetic energy - Initial kinetic energy
The final kinetic energy is zero since the van comes to rest. Therefore:
Work = 0 - 8437.5 J = -8437.5 J
Now we can calculate the average force using the formula:
Average Force = Work / Distance
Plugging in the values:
Average Force = -8437.5 J / 0.50 m
Evaluating the expression:
Average Force = -16875 N (Newtons)
Since force is a vector quantity, we don't consider the negative sign in this case.
Therefore, the average force exerted by the seat belt on the passenger during the crash was 16875 Newtons.