Collision, Using Momentum Principles

[leejqs]

Homework Statement

In a crash test, a truck with a mass of 2500 kg traveling at 25 m/s smashes head-on into a concrete wall without rebounding. The front end crumples so much that the truck is 0.65 m shorter than before. What is the average speed of the truck during the collision (that is, during the interval between first contact with the wall and coming to a stop)? About how long does the collision last? What is the magnitude of the average force exerted by the wall on the truck during the collision? It is interesting to compare this force to the weight of the truck. Calculate the ratio of the force of the wall to the gravitational force mg on the truck. (This large ratio shows why a collision is so damaging.)

Homework Equations

p=F*T
or... Change in momentum=Net Force times Change in Time

The Attempt at a Solution

I really have no idea where to start this problem...

 

[anathema]

Hello! Let's break this problem down step by step. First, we need to understand the given information. We have a truck with a mass of 2500 kg traveling at a speed of 25 m/s. It collides head-on with a concrete wall and does not rebound. The front end of the truck crumples, resulting in a decrease in length of 0.65 m. We want to find the average speed of the truck during the collision, the duration of the collision, and the magnitude of the average force exerted by the wall on the truck.

To solve this problem, we will use the equation: p = F * t, where p is the change in momentum, F is the net force, and t is the change in time. We can also use the equation: F = ma, where F is the force, m is the mass, and a is the acceleration.

First, let's find the change in momentum of the truck. We know that momentum is equal to mass times velocity, so we can calculate the initial momentum of the truck before the collision as follows:

p(initial) = m * v
= (2500 kg) * (25 m/s)
= 62,500 kg*m/s

Next, we need to find the final momentum of the truck after the collision. Since the truck comes to a complete stop, the final momentum will be zero. So, the change in momentum can be calculated as:

p(final) = 0 kg*m/s

Now, we can use the equation p = F * t to find the average force exerted by the wall on the truck. We know the change in momentum (p) and the change in time (t), so we can rearrange the equation to solve for force (F):

F = p/t

Substituting the values we calculated earlier, we get:

F = (62,500 kg*m/s) / t

Next, we need to find the duration of the collision (t). We can do this by using the information given in the problem. We know that the front end of the truck crumples by 0.65 m, so the distance traveled during the collision is 0.65 m. We also know the initial speed of the truck (25 m/s). We can use the equation: d = v*t to find the time (t):

t = d/v
= (0.65 m) / (

 

[kerimek]

I would approach this problem by first identifying the relevant principles and equations that can be used to solve it. In this case, we can use the principles of momentum and force, and the equation p=F*T, or change in momentum equals net force times change in time.

Next, we can gather the necessary information from the given data. We know the mass of the truck (2500 kg), its initial velocity (25 m/s), and the distance it crumples (0.65 m). We also know that the truck comes to a complete stop after the collision.

Using the equation p=F*T, we can calculate the change in momentum of the truck by multiplying its mass (2500 kg) by its initial velocity (25 m/s), which gives us a value of 62,500 kg*m/s. This is also equal to the force exerted on the truck by the wall multiplied by the duration of the collision.

To find the average speed of the truck during the collision, we can use the equation v=Δx/Δt, where v is the average speed, Δx is the change in position (0.65 m), and Δt is the duration of the collision. Rearranging the equation, we get Δt=Δx/v. Plugging in the values, we get Δt=0.65 m/(25 m/s)=0.026 s. Therefore, the collision lasts for approximately 0.026 seconds.

To calculate the average force exerted by the wall on the truck, we can use the equation F=Δp/Δt, where F is the force, Δp is the change in momentum (62,500 kg*m/s), and Δt is the duration of the collision (0.026 s). Plugging in the values, we get F=62,500 kg*m/s/0.026 s=2,403,846.15 N.

Finally, we can calculate the ratio of the force of the wall to the weight of the truck by dividing the force by the truck's weight (2500 kg*9.8 m/s^2). This gives us a ratio of 2403.85, showing that the force exerted by the wall is significantly larger than the weight of the truck. This explains why collisions can be so damaging.

In conclusion, using the principles of momentum and force, we were able to calculate the average speed of