Work/Kinetic energy, running a race with mass and speed

In summary, the problem is asking to find the mass of the friend who is beating the person in a race with the given information that their kinetic energies were initially equal and after a 21% increase in speed, their speeds became equal. The equation used is KE=1/2mv^2 and two equations are needed to solve for the friend's mass.
  • #1
Willy_Kingston
1
0

Homework Statement


You run a race with your friend. At first you each have the same kinetic energy, but then you find that she is beating you. When you increase your speed by 21%, you are running at the same speed she is. If your mass is 81 kg, what is her mass?
Your mass: 81kg
Your speed is increased by 21%
Her speed:?

Homework Equations


KE=1/2mv2



The Attempt at a Solution


1/2mv2=1/2mv2
1/2(81)v2=1/2?v2
 
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  • #2
Willy_Kingston said:
1/2mv2=1/2mv2
That's not a terribly useful equation. Try using different symbols for different variables, e.g. the two masses and the two speeds. If you find subscripting a pain, combine upper and lower case, like Ma, Mb.
 
  • #3
Willy_Kingston said:
1/2mv2=1/2mv2
1/2(81)v2=1/2?v2


Apart from the fact that you should give different names, you are considering both kinetic energy and speed equal at the same time... but it is not what the problem asks you...

When kinetic energy is the same, speeds are different; speeds are equal after you increasing speed. You will need two equations for solving this
Hint: write in equations the two different informations I gave you... it will solve by itself then :smile:
 

1. What is work and kinetic energy?

Work is defined as the force applied to an object multiplied by the distance it moves in the direction of that force. Kinetic energy is the energy an object possesses due to its motion.

2. How is work related to kinetic energy?

Work is directly related to kinetic energy. When work is done on an object, its kinetic energy increases. On the other hand, when work is done by an object, its kinetic energy decreases.

3. How does mass affect the work and kinetic energy in a race?

Mass does not directly affect the work and kinetic energy in a race. However, a runner with a larger mass will require more work to be done on them in order to achieve the same amount of kinetic energy as a runner with a smaller mass.

4. How does speed affect the work and kinetic energy in a race?

Speed has a direct impact on both work and kinetic energy in a race. The faster a runner moves, the more work is done on them and the higher their kinetic energy. This is because kinetic energy is directly proportional to the square of an object's velocity.

5. How can work and kinetic energy be calculated in a race?

Work can be calculated by multiplying the force applied to an object by the distance it moves in the direction of that force. Kinetic energy can be calculated using the formula 1/2 * mass * velocity^2. In a race, the work done by a runner can be calculated by multiplying their weight by the distance they ran, and their kinetic energy can be calculated using their mass and average speed throughout the race.

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