The front 1.20 m of a 1,350-kg car is designed as a "crumple zone" that collapses to absorb the shock of a collision.
(a) If a car traveling 21.0 m/s stops uniformly in 1.20 m, how long does the collision last?
s
(b) What is the magnitude of the average force on the car?
N
(c) What is the magnitude of the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.
g
a) x = 1/2(vo + vf)t
vf is zero
b)Ft = change mv
mv final is again zero
c) F = ma
To find out the answers to these questions, we can use the equations of motion for uniformly decelerated motion.
Given:
Initial velocity, u = 21.0 m/s
Final velocity, v = 0 (the car stops)
Displacement, s = 1.20 m
Mass, m = 1,350 kg
Acceleration due to gravity, g = 9.8 m/s^2
(a) To find the time duration of the collision, we can use the equation:
s = ut + (1/2)at^2
Since the final velocity is zero, we have:
0 = u*t + (1/2)at^2
Simplifying the equation for time, t, we get:
t = (2s) / a
Substituting the given values, we have:
t = (2 * 1.20) / a
(b) To find the magnitude of the average force on the car, we can use the equation:
F = ma
Substituting the given values, we have:
F = (1,350 kg) * a
(c) To find the magnitude of the acceleration of the car in terms of the acceleration due to gravity, we can use the equation:
a = g * a_g
Substituting the given values, we have:
a = (9.8 m/s^2) * a_g
Now, we'll calculate each answer step-by-step:
(a) To find the time duration of the collision:
t = (2 * 1.20) / a
(b) To find the magnitude of the average force:
F = (1,350 kg) * a
(c) To find the magnitude of the acceleration:
a = (9.8 m/s^2) * a_g
Now, we can calculate each value one by one. Let's start with part (a).
To solve these questions, we will use the principles of motion and Newton's laws of motion.
(a) To find the time taken during the collision, we can use the equation:
v^2 = u^2 + 2as
where v is the final velocity (0 m/s in this case), u is the initial velocity (21.0 m/s), a is the acceleration, and s is the displacement (1.20 m).
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the given values, we get:
a = (0 - (21.0 m/s)^2) / (2 * 1.20 m)
Calculating this expression gives us the acceleration during the collision.
(b) The magnitude of average force can be determined using Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
F = m * a
Substituting the known values, we can calculate the average force.
(c) Finally, the magnitude of the acceleration of the car can be expressed as a multiple of the acceleration due to gravity (g). Divide the calculated acceleration by g to determine the ratio.