Kinetic Energy/Velocity Relationship

In summary, one car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 5.7 m/s, they then have the same kinetic energy. By taking the ratio of the equations for each car's kinetic energy, we can determine the relationship between their original speeds. Using this relationship, we can solve for the original speeds of the two cars.
  • #1
bmyer
2
0

Homework Statement


One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 5.7 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?


Homework Equations


KE=1/2mv^2, where KE equals kinetic energy.


The Attempt at a Solution


Don't know where to start.
Car 1: .5KE=(1/2)(m)(v1^2)
Car 2: KE = (1/2)(.5m)(v2^2)

You can set the 2 equations equal in KE when 5.7 is added to both v1 and v2, but there are still too many variables! I have been stuck on this problem for 2 hours and I am about to go crazy! Please help!
 
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  • #2
Car 1: .5KE=(1/2)(m)(v1^2)
Car 2: KE = (1/2)(.5m)(v2^2)

Take the ratio of the above two equations. You get the relation between V1 and V2.
You can set the 2 equations equal in KE when 5.7 is added to both v1 and v2
Use the above relation to solve the next two equations.
 
  • #3


I would approach this problem by first identifying the known variables and using the given equations to solve for the unknown variables. In this case, we know that one car has twice the mass of the other, and that both cars increase their speed by 5.7 m/s. We can use the equation KE=1/2mv^2 to calculate the initial kinetic energy of each car before the speed increase.

For Car 1, we can write the equation as KE1=1/2(2m)(v1^2), where KE1 represents the initial kinetic energy and v1 represents the initial speed. Similarly, for Car 2, we can write the equation as KE2=1/2(m)(v2^2), where KE2 represents the initial kinetic energy and v2 represents the initial speed.

Since we know that the initial kinetic energy for Car 1 is half that of Car 2, we can set up the following equation: KE1 = 1/2(KE2). This means that 1/2(2m)(v1^2) = 1/2(m)(v2^2), which simplifies to m(v1^2) = 1/2m(v2^2).

Next, we can use the information that both cars increase their speed by 5.7 m/s to set up another equation. We know that after the speed increase, both cars have the same kinetic energy. This can be written as KE1 + 1/2(2m)(5.7)^2 = KE2 + 1/2(m)(5.7)^2. Simplifying this equation, we get 2m(v1^2) + 32.49m = m(v2^2) + 16.245m.

Now we have two equations with two unknowns (v1 and v2). We can solve for one variable in terms of the other and substitute it into the other equation to solve for the remaining variable. In this case, we can solve for v1 in terms of v2 using the first equation, which gives us v1 = √(1/2v2^2). Substituting this into the second equation, we get 2m(1/2v2^2) + 32.49m = mv2^2 + 16.245m. Simplifying, we get
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is a scalar quantity that depends on the mass and velocity of the object.

2. How is kinetic energy related to velocity?

The kinetic energy of an object is directly proportional to the square of its velocity. This means that as the velocity increases, the kinetic energy also increases, and vice versa.

3. What is the formula for calculating kinetic energy?

The formula for kinetic energy is KE = 1/2 * m * v^2, where KE is kinetic energy, m is the mass of the object, and v is the velocity.

4. How does the velocity affect the amount of kinetic energy?

The amount of kinetic energy an object has is directly proportional to the square of its velocity. This means that doubling the velocity will quadruple the kinetic energy, while halving the velocity will reduce the kinetic energy to one-fourth.

5. Why is understanding the kinetic energy/velocity relationship important?

Understanding the kinetic energy/velocity relationship is important because it allows us to predict the impact and force of moving objects. It also helps us understand the concept of energy and how it is transformed from one form to another.

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