Total Kinetic Energy: Solving 72 kg Person Running at 12 km/h

In summary: So the final answer should be 400 J.In summary, the conversation discusses the proportions of a person's mass attributed to their arms and legs, and how to calculate the total kinetic energy of a person running with specific arm and leg lengths. The student is having trouble with sig figs in their calculations, and it is determined that they have not included the kinetic energy due to rotation and have not used the correct number of sig figs in their conversions and final answer. The correct answer is 400 J.
  • #1
mdewdude
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0

Homework Statement



Biomedical measurements show that the arms and hands together typically make up 13.0 % of a person's mass, while the legs and feet together account for 37.0 %. For a rough (but reasonable) calculation, we can model the arms and legs as thin uniform bars pivoting about the shoulder and hip, respectively. Let us consider a 72.0 kg person having arms 65.0 cm long and legs 90.0 cm long. The person is running at 12.0 km/h, with his arms and legs each swinging through 30 decrees }. Assume that the arms and legs are kept straight.

What is the total kinetic energy due to both his forward motion and his rotation?

Homework Equations



0.5 m v^2 =KE

The Attempt at a Solution


This is for online hw. The problem is that no matter how i do the sig figs for this problem, i still get it wrong.

After converting the 12 km/h the proper sig figs indicated a m/s value of 3 m/s. by plugging that into the equation i get 72kg*9m/s *0.5=300j but if i do it like this 72 kg*3.333^2 *0.5=400 but the 300 j answer is wrong but the 400 j answer is wrong but due to sig figs or rounding. Can somebody help me and tell me what is wrong?
 
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  • #2
There are two problems I see here.

1. You haven't included the kinetic energy due to rotation of the arms and legs.

2. "12 km/h" has two sig figs, so the conversion to m/s should also have two sig figs, i.e. 3.3 m/s, not 3 m/s. And the final answer would have two sig figs, since the mass "72 kg" also has two sig figs.
 
  • #3




The issue with your solution is that you are using the incorrect value for velocity. The problem states that the arms and legs each swing through 30 degrees, which means that the velocity is not constant. In order to accurately calculate the kinetic energy, you will need to use the average velocity for the swinging motion. This can be calculated by dividing the total distance traveled (in this case, the length of the arms or legs) by the time taken to complete the swing (which can be approximated as half of the period of the swinging motion). Once you have the average velocity, you can use that value in the equation 0.5mv^2 to calculate the kinetic energy. Remember to use the proper units (m/s) for velocity. I hope this helps!
 

1. How do you calculate total kinetic energy?

Total kinetic energy is calculated by multiplying the mass of an object by its velocity squared and then dividing by two. This can be represented by the formula E = 1/2 * m * v^2.

2. What is considered the standard unit for kinetic energy?

The standard unit for kinetic energy is joules (J). However, in some cases, other units such as calories or electronvolts may also be used.

3. How do you convert kilometers per hour to meters per second?

To convert from kilometers per hour (km/h) to meters per second (m/s), divide the speed in km/h by 3.6. So in this case, 12 km/h would be equal to 3.33 m/s.

4. Is kinetic energy affected by direction of motion?

Yes, kinetic energy is affected by direction of motion. The direction of motion determines the sign of the velocity and therefore can affect the overall value of kinetic energy. For example, if an object is moving in the opposite direction, the kinetic energy would be negative.

5. How does the mass of an object impact its kinetic energy?

The mass of an object has a direct impact on its kinetic energy. The larger the mass, the greater the kinetic energy, assuming the velocity remains the same. This is because the mass is directly proportional to the kinetic energy in the formula E = 1/2 * m * v^2.

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