A 500 kg automobile travelling at 30 m/s strikes a 100kg stationary pedestrian. The impact duration is 0.1 s and it slows the automobile by 1m/s. Calculate:
a. the velocity imparted to the pedestrian
b. the force exerted by the vehicle on the pedestrian.(Ans=5000N)
initial momentum = 500 * 30 + 100 * 0 =15,000 kg m/s
final momentum = 500 * 29 + 100 * u = 14,500 + 100 u
but they are the same, no momentum was removed from the system.
so
15,000 = 14,500 + 100 u
u = 5 m/s
It did not hit the pedestrian very hard. In fact they would be more likely to stick together.
force = rate of change of momentum
= 100 *5 / .1 = 5000 kg m/s^2 = 5,000 Newtons
Given:
M1 = 500 kg, V1 = 30 m/s.
M2 = 100 kg, V2 = 0.
V3 = 30-1 = 29 m/s = Velocity of car after collision.
V4 = Velocity of person after collision.
a. Momentum before = momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V4.
500*30 + 100*0 = 500*29 + 100*V4,
V4 = 5 m/s.
b. V 4 = V2 + a*t .
5 = 0 + 0.1a,
a = 50 m/s^2.
F = M*a = 100 * 50 = 5,000 N.
To calculate the velocity imparted to the pedestrian and the force exerted by the vehicle on the pedestrian, we can use the principles of conservation of momentum and the formula for force.
a. To find the velocity imparted to the pedestrian, we can use the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
Momentum of the automobile = mass of the automobile * velocity of the automobile
Momentum of the automobile = 500 kg * 30 m/s = 15,000 kg·m/s
The pedestrian is stationary before the collision, so their momentum is 0 kg·m/s.
After the collision:
The automobile slows down by 1 m/s, so the velocity of the automobile after the collision is (30 m/s - 1 m/s) = 29 m/s.
Let's assume the pedestrian gains a velocity of v m/s.
The momentum of the automobile after the collision = mass of the automobile * velocity of the automobile after the collision
Momentum of the automobile after the collision = 500 kg * 29 m/s = 14,500 kg·m/s
The momentum imparted to the pedestrian = mass of the pedestrian * velocity imparted to the pedestrian
Momentum imparted to the pedestrian = 100 kg * v kg·m/s
According to the conservation of momentum principle, the total momentum before the collision (15,000 kg·m/s) is equal to the total momentum after the collision (14,500 kg·m/s + 100 kg * v kg·m/s).
15,000 kg·m/s = 14,500 kg·m/s + 100 kg * v kg·m/s
Now, by rearranging the equation, we can solve for the velocity imparted to the pedestrian:
100 kg * v kg·m/s = 15,000 kg·m/s - 14,500 kg·m/s
100 kg * v kg·m/s = 500 kg·m/s
v = 500 kg·m/s / 100 kg
Therefore, the velocity imparted to the pedestrian is 5 m/s.
b. To find the force exerted by the vehicle on the pedestrian, we can use the formula for force:
Force = change in momentum / time
The change in momentum is given by:
Change in momentum = mass of the pedestrian * velocity imparted to the pedestrian
Change in momentum = 100 kg * 5 m/s = 500 kg·m/s
The given impact duration is 0.1 s.
Now, we can calculate the force:
Force = change in momentum / time
Force = 500 kg·m/s / 0.1 s
Force = 5000 N
Therefore, the force exerted by the vehicle on the pedestrian is 5000 Newtons (N).