Kinetic energy and work

In summary, a father and son, with the father having half the kinetic energy and double the mass of the son, are racing. If the father speeds up by 1.0m/s, he will have the same kinetic energy as the son. The original speeds of the father and son can be found by solving the quadratic equation -Vd^2 +2Vd + 1 = 0.
  • #1
netrunnr
15
0
A father racing his son has half the kinetic energy of the son who has half the mass of the father. The father speeds up by 1.0m/s and then has the same kinetic energy as the son. what are the original speeds of the father and the son?
using k=1/2mv^2 and solving for v I did this:

M = mass K = kinetic energy V=velocity
d = (dad) father s = son i = initial f=final

Initial father
Md
Kdi
Vd

Initial son
Ms = 1/2 Md
Ks = 2Kdi
Vs

Kd = 1/2 Md (Vd )^2
Ks = 1/2 1/2 Md (Vd) ^2
2(1/2 Md (Vd)^2 = 1/2 1/2 Md Vs^2
2(2Vd^2 = 1/2 Vs^2
4Vd^2 = 1Vs^2

Final father
Md
Kdf
Vd+1.0ms
Final Son
Ms = 1/2 Md
Ks = Kdf
Vs

Kd = 1/2 Md (Vd +1)^2
Ks = 1/2 1/2 Md (V2)^2
1/2Md ( Vd +1)^2 = 1/2 1/2 Md Vs^2
now taking from initial the 4Vd^2 = 1Vs^2
(Vd +1)^2 = 1/2Vs^2
(Vd +1) ^2 = 1/2 4Vd^2
Vd^2 +2Vd + 1 = 2Vd^2
Vd^2 + 2Vd + 1 -2Vd^2 = 0
-Vd^2 +2Vd + 1 =0

I was trying to solve it at this point like a quadratic equation but I am lost because it seems unsolvable. I know I made a mistake and can't see where...
 
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  • #2
Hi netrunnr,

netrunnr said:
A father racing his son has half the kinetic energy of the son who has half the mass of the father. The father speeds up by 1.0m/s and then has the same kinetic energy as the son. what are the original speeds of the father and the son?
using k=1/2mv^2 and solving for v I did this:

M = mass K = kinetic energy V=velocity
d = (dad) father s = son i = initial f=final

Initial father
Md
Kdi
Vd

Initial son
Ms = 1/2 Md
Ks = 2Kdi
Vs

Kd = 1/2 Md (Vd )^2
Ks = 1/2 1/2 Md (Vd) ^2

This is a typo; it should be Vs. (But it looks like you correct it in the next line.)

2(1/2 Md (Vd)^2 = 1/2 1/2 Md Vs^2
2(2Vd^2 = 1/2 Vs^2

I don't believe this is correct, but it is probably just a typo because the next line is correct.

4Vd^2 = 1Vs^2

This line is correct, and so once you find the initial speed of the dad Vd, you can find the speed of the son.

Final father
Md
Kdf
Vd+1.0ms
Final Son
Ms = 1/2 Md
Ks = Kdf
Vs

Kd = 1/2 Md (Vd +1)^2
Ks = 1/2 1/2 Md (V2)^2
1/2Md ( Vd +1)^2 = 1/2 1/2 Md Vs^2
now taking from initial the 4Vd^2 = 1Vs^2
(Vd +1)^2 = 1/2Vs^2
(Vd +1) ^2 = 1/2 4Vd^2
Vd^2 +2Vd + 1 = 2Vd^2
Vd^2 + 2Vd + 1 -2Vd^2 = 0
-Vd^2 +2Vd + 1 =0

I was trying to solve it at this point like a quadratic equation but I am lost because it seems unsolvable. I know I made a mistake and can't see where...

It looks right to me. Just put it in the quadratic equation and solve. What do you get?
 
  • #3


I would like to clarify that kinetic energy and work are two different concepts. Kinetic energy is the energy an object possesses due to its motion, while work is the energy transferred to or from an object by a force acting on it.

Now, let's address the problem at hand. We are given that the father has half the kinetic energy of the son, and that the father speeds up by 1.0 m/s to have the same kinetic energy as the son. From this information, we can set up the following equations:

Kd = 1/2 Md Vd^2 (father's initial kinetic energy)
Ks = 2Kd = 1/2 Ms Vs^2 (son's initial kinetic energy)
Kdf = Ks = 1/2 Md (Vd+1)^2 (father's final kinetic energy)
Kdf = 1/2 Ms Vs^2 (son's final kinetic energy)

Now, we can solve for the initial velocity of the father (Vd) using the first two equations:

Kd = 1/2 Md Vd^2
Ks = 1/2 Ms Vs^2
1/2 Md Vd^2 = 1/2 (1/2 Md) Vs^2
Vd^2 = 1/2 Vs^2
Vd = √(1/2 Vs^2) = Vs/√2

Next, we can substitute this value of Vd into the third and fourth equations to solve for the final velocities:

Kdf = 1/2 Md (Vd+1)^2
Kdf = 1/2 (1/2 Md) (Vs/√2 + 1)^2
1/2 Md (Vd+1)^2 = 1/2 (1/2 Md) (Vs^2/2 + Vs + 1)
Vd^2 + 2Vd + 1 = (Vs^2/4 + Vs + 1)
Vs^2/4 + 2Vs + 1 = Vs^2/4 + Vs + 1
Vs = 0

Therefore, the initial velocity of the father (Vd) is Vs/√2 = 0, and the initial velocity of the son (Vs) is also 0. This means that both the father and
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is dependent on the mass and velocity of the object, and is calculated using the formula KE = 1/2 mv^2, where m is the mass and v is the velocity.

2. How is kinetic energy different from potential energy?

Kinetic energy is the energy an object has due to its motion, while potential energy is the energy an object has due to its position or state. Kinetic energy is the energy an object has when it is in motion, while potential energy is the energy an object has when it is at rest and has the potential to move.

3. What is the relationship between kinetic energy and work?

Work is the transfer of energy from one object to another. When a force is applied to an object, work is done and the object gains kinetic energy. The work done on an object is equal to the change in its kinetic energy.

4. How does kinetic energy affect an object's motion?

Kinetic energy is directly proportional to an object's velocity. This means that as an object's kinetic energy increases, its velocity also increases. Therefore, the more kinetic energy an object has, the faster it will be moving.

5. Can kinetic energy be converted into other forms of energy?

Yes, kinetic energy can be converted into other forms of energy such as heat, sound, or potential energy. For example, when a moving object collides with another object, its kinetic energy is transferred and can be converted into sound energy if the collision produces a sound.

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