a truck weighting 20000 pounds going 5 mph what is the force of the truck when it hits a person and comes to a complete stop?
To find the force exerted by the truck when it hits a person and comes to a complete stop, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
1. First, convert the weight of the truck from pounds to mass in slugs (since the unit of force used in the US customary system is pounds-force).
1 pound = 1 slug (approximately)
Therefore, the truck's mass (m) would be 20000 pounds.
2. Next, we need to calculate the acceleration of the truck. Since the truck comes to a complete stop, it decelerates to zero velocity. We can use the following kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 mph since the truck comes to a complete stop)
u = initial velocity (5 mph)
a = acceleration
s = distance traveled (unknown)
Rearranging the equation:
a = (v^2 - u^2) / (2s) ...(Equation 1)
3. As we know that the truck travels in a straight line and comes to a stop after hitting the person, we can assume a typical stopping distance of around 3-4 feet (or 1-1.2 meters).
4. Convert the initial velocity from mph to ft/s.
1 mph = 1.47 ft/s (approximately)
Therefore, the initial velocity (u) would be 5 mph * 1.47 = 7.35 ft/s (approximately).
5. Now, we can substitute the known values into Equation 1 to calculate the acceleration (a).
a = (0^2 - 7.35^2) / (2 * 3 ft)
6. Calculate the resulting acceleration.
7. Finally, we can calculate the force (F) using Newton's second law:
F = m * a
Please note that the actual force experienced by the person during such an impact can vary depending on various factors, such as the type of collision, contact area, and other variables.
To determine the force exerted by the truck when it hits a person and comes to a complete stop, you need to calculate the force using the concept of impulse.
The formula for impulse is:
Impulse = Force × Time
Since the truck comes to a complete stop, the time taken for the truck to come to rest is important. However, this information is not provided in your question. Instead, we will consider that the time taken for the truck to stop is very small (almost instantaneous).
Let's consider the concept of impulse further. Impulse is also equal to the change in momentum. So, we can rewrite the formula using the concept of momentum:
Impulse = Change in Momentum
Momentum = Mass × Velocity
Initial momentum of the truck = Mass × Initial Velocity
Final momentum of the truck = Mass × Final Velocity
The initial velocity of the truck is 5 mph, but it is not specified in which direction the truck is moving. For simplicity, let's assume the truck is moving in a straight line towards the person.
Converted to feet per second (since we are working with pounds), the initial velocity of the truck is approximately 7.33 ft/s:
Initial Velocity = 5 mph = 5 × 1.467 ft/s = 7.33 ft/s
The initial momentum of the truck is:
Initial Momentum = Mass × Initial Velocity
= 20000 lb × 7.33 ft/s
Now, since the truck comes to a complete stop, the final velocity is zero ft/s:
Final Velocity = 0 ft/s
The final momentum of the truck is:
Final Momentum = Mass × Final Velocity
= 20000 lb × 0 ft/s
= 0 lb·ft/s
The change in momentum is then:
Change in Momentum = Final Momentum - Initial Momentum
= 0 lb·ft/s - (20000 lb × 7.33 ft/s)
Finally, the force exerted by the truck can be calculated using the formula:
Force = Change in Momentum / Time
However, as mentioned earlier, the time taken for the truck to stop is not provided. Without this information, it is not possible to calculate the force. To determine the force, you would need to know the stopping time or additional information about the collision.