A car and a truck are both travelling at the speed limit of 60 km h^-1 but in opposite directi

A car and a truck are both travelling at the speed limit of...

A car and a truck are both travelling at the speed limit of $60 \mathrm{~km} \mathrm{~h}^{-1}$ but in opposite directions as shown. The truck has twice the mass of the car. (Figure Cant Copy) The vehicles collide head-on and become entangled together. a) During the collision, how does the force exerted by the car on the truck compare with the force exerted by the truck on the car? Explain. b) In what direction will the entangled vehicles move after collision, or will they be stationary? Support your answer, referring to a physics principle. c) Determine the speed (in $\mathrm{km} \mathrm{h}^{-1}$ ) of the combined wreck immediately after the collision. d) How does the acceleration of the car compare with the acceleration of the truck during the collision? Explain. e) Both the car and truck drivers are wearing seat belts. Which driver is likely to be more severely jolted in the collision? Explain. f) The total kinetic energy of the system decreases as a result of the collision. Is the principle of conservation of energy violated? Explain.

A car and a truck are both travelling at the speed limit of $60 \mathrm{~km} \mathrm{~h}^{-1}$ but in opposite directions as shown. The truck has twice the mass of the car.
(Figure Cant Copy)
The vehicles collide head-on and become entangled together.
a) During the collision, how does the force exerted by the car on the truck compare with the force exerted by the truck on the car? Explain.
b) In what direction will the entangled vehicles move after collision, or will they be stationary? Support your answer, referring to a physics principle.
c) Determine the speed (in $\mathrm{km} \mathrm{h}^{-1}$ ) of the combined wreck immediately after the collision.
d) How does the acceleration of the car compare with the acceleration of the truck during the collision? Explain.
e) Both the car and truck drivers are wearing seat belts. Which driver is likely to be more severely jolted in the collision? Explain.
f) The total kinetic energy of the system decreases as a result of the collision. Is the principle of conservation of energy violated? Explain.

Key Concepts

Energy Transformation and Conservation

While kinetic energy might not be conserved in inelastic collisions, the law of conservation of energy remains valid overall. The lost kinetic energy in collisions is converted into other forms (such as heat, sound, and energy used in permanent deformation) and is not destroyed, thereby ensuring that the total energy of the system remains constant.

Mass and Acceleration Relationships

Due to Newton's Second Law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In collisions, even if the same magnitude of force is applied on both objects, the object with the smaller mass will experience a higher acceleration, leading to more pronounced deceleration or acceleration.

Inelastic Collisions

An inelastic collision is one in which the colliding objects stick together after the impact, resulting in a loss of kinetic energy. Although kinetic energy is not conserved, momentum conservation still applies. The loss in kinetic energy is usually transformed into other forms of energy such as heat or deformation work.

Conservation of Momentum

Momentum, defined as the product of mass and velocity, remains conserved in an isolated system. In collision problems, even in cases where kinetic energy is not wholly conserved, the total momentum before collision equals the total momentum after collision. This principle is used to determine the velocity of colliding objects after impact, especially when they become entangled.

Newton's Third Law

This principle states that for every action there is an equal and opposite reaction. In the context of collisions, it means that the force exerted by one vehicle on the other has the same magnitude as the force exerted in the opposite direction, regardless of the mass differences between the vehicles.

Transcript

00:01 Okay, so in this scenario we're told we have a car and a truck traveling both at the same speed limit of 60 kilometers per hour but in opposite directions.

00:08 The truck has twice the mass of the car.

00:11 So we can call the car's mass m1, the truck's mass would be 2m1, double the size.

00:17 Now, the vehicles collide head -on and become entangled.

00:21 During this collision, how do the forces exerted by each other compare? so, if we take a look, we know we can use the equation f equals ma, right? so in this case, let's take a look at the forces exerted by each of the vehicles.

00:36 So f equals m1a would be the force exerted by the car and then the force exerted by the truck would be 2m1a because we know that really it's m2, but m2 is 2 times the size of m1.

00:56 So it's gonna be double the force.

00:58 So we know that the truck is gonna exert more force on the car than the car will exert on the force.

01:04 Okay, in what direction will the entangled vehicles move after the collision or will they be stationary? so they will not be stationary and the direction they will move will be the motion that the truck had to begin with, right? and we can double check that using our momentum equations, our conservation of momentum.

01:22 We know that m1v1 plus m2v2 is equal to the combined mass of m1 plus m2 times v3, which we'll call the velocity of the entangled collision, if you will, after they've come together.

01:41 Now we know that m2 is 2m1 and we know that v is 60 and v2 is negative 60 so we can express this as 60m1 minus, right, because m2 is 2m and v is negative 60, so minus 2 times negative 60 is equal to 3m1v3.

02:10 Okay.

02:12 We know that all the m's will cancel out and we're gonna get 60 minus 2 times 60, which is negative 60 and negative 60 is equal to 3v3, dividing by 3, v3 equals negative 20 kilometers per hour.

02:32 So this is negative because we've just decided that the car's vehicle speed was positive...

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