How Does a Car's Momentum Change If Its Kinetic Energy Doubles?

[Lolagoeslala]

Homework Statement

A car (of constant mass) doubles its kinetic energy while driving down a hill sloped at 45º. The factor by which its momentum changes is answer is 1.4?

 

[Doc Al]

The factor by which its momentum changes is answer is 1.4?

Yes. The factor is √2 ≈ 1.41

 

[Lolagoeslala]

Yes. The factor is √2 ≈ 1.41

Would u get how u got that?

1/2mv^2 = P right?

 

[Doc Al]

$${KE}_1 = 1/2 m v^2_1$$
$${KE}_2 = 2 {KE}_1$$
Find v₂ in terms of v₁.

 

[Nickie]

I would like to clarify and provide additional information about the concepts of kinetic energy and momentum.

Kinetic energy is the energy an object possesses due to its motion. It is directly proportional to the mass and the square of the velocity of the object. In this scenario, the car doubles its kinetic energy, meaning its mass and/or velocity must have increased.

On the other hand, momentum is the product of an object's mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. In this case, the factor by which the car's momentum changes is not 1.4, but rather 2. This is because momentum is directly proportional to both mass and velocity, so doubling the kinetic energy would result in a doubling of momentum as well.

Furthermore, the slope of the hill does not affect the change in momentum, as long as the car is moving at a constant speed. This is because the gravitational force acting on the car is perpendicular to the direction of motion, so it does not contribute to the change in momentum.

In conclusion, while the car's kinetic energy may double while driving down a hill, its momentum will also double, resulting in a factor of 2, not 1.4. It is important to understand and accurately apply these concepts in order to fully grasp the behavior of objects in motion.