A 750 kg car traveling 22.0 m/s due north crashes into a 1500 kg truck traveling 20 m/s due west. The two vehicles become locked together and travel 19.0 m before stopping. Find the average frictional force (magnitude and direction) that brings the two to a stop.
p1=m1•v1
p2=m2•v2
p12=sqrt(p1²+p2²)
v= p12/(m1+m2) = sqrt(p1²+p2²)/(m1+m2)
mv²/2 =F(fr) •s
F(fr) = mv²/2•s
32233
ewewewec
To find the average frictional force that brings the two vehicles to a stop, we need to consider the principle of conservation of momentum.
First, let's calculate the initial momentum of both vehicles separately. The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
Momentum of car = mass of car × velocity of car
= 750 kg × 22.0 m/s
= 16,500 kg·m/s (due north)
Momentum of truck = mass of truck × velocity of truck
= 1500 kg × -20.0 m/s (since the truck is traveling west, its velocity is negative)
= -30,000 kg·m/s (due west)
Now that we have the initial momentum of each vehicle, we can calculate the total initial momentum by adding these two momenta together:
Total initial momentum = Momentum of car + Momentum of truck
= 16,500 kg·m/s (due north) + (-30,000 kg·m/s) (due west)
To add the momenta, we need to break them into their x and y-components. Since the car is traveling due north and the truck is traveling due west, the only nonzero components are the y-component for the car and the x-component for the truck.
Momentum of car (y-component) = 16,500 kg·m/s (due north)
Momentum of truck (x-component) = -30,000 kg·m/s (due west)
Next, we calculate the final momentum of the combined system. Since the cars become locked together and move 19.0 m before stopping, their final velocity is 0 m/s. Thus, the final momentum is zero:
Total final momentum = 0 kg·m/s
According to the principle of conservation of momentum, the total initial momentum and total final momentum are equal:
Total initial momentum = Total final momentum
Now, let's break down the total initial and final momenta into their components:
Total initial momentum = Momentum of car (y-component) + Momentum of truck (x-component)
Total final momentum = Momentum of car (y-component) + Momentum of truck (x-component)
Substituting the calculated momenta into these equations, we get:
16,500 kg·m/s (due north) + (-30,000 kg·m/s) (due west) = 0 kg·m/s
To find the average frictional force that brings the two vehicles to a stop, we need to find the change in momentum and divide it by the time it took for the change to occur. However, we don't have the time information in this problem.
Therefore, we cannot determine the average frictional force without the time component.