Find Tension & Force Exerted by Shinbones on Foot w/ W, a, & b

In summary, the problem involves finding the tension in the calf muscle and the force exerted by the shinbones on the bones of the foot. These values can be expressed in terms of W, a, and b, with W being the person's weight and a and b representing the distance between the back and front of the foot respectively. To solve this problem, it is suggested to write two equations - one for the total force on the foot being zero and another for the total torque on the foot being zero - and solve for the unknown values. It is also recommended to draw a diagram and identify the forces at play before attempting to write the equations.
  • #1
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Homework Statement



A person of weight W stands on the ball of one foot. Find
the tension in the calf muscle and the force exerted by the shinbones
on the bones of the foot, in terms of W, a, and b. (The tension is a
measure of how tight the calf muscle has been pulled; it has units
of Newtons, and equals the amount of force applied by the muscle
where it attaches to the heel.) For simplicity, assume that all the
forces are at 90-degree angles to the foot. Suggestion: Write down
an equation that says the total force on the foot is zero, and another
equation saying that the total torque on the foot is zero; solve the
two equations for the two unknowns

Homework Equations





The Attempt at a Solution


I'm not sure what to do for this one.Am I suppose to do W=a*b?
 
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  • #2
Well, you need to tell us what a and b are before we can help you.

It's a very good idea to start out by drawing a picture (even if it's relatively crude) and identifying forces. I would suggest trying to stand on one foot. You'll find out interesting things like your center of gravity has to be above your foot or you'll fall over. It also might help you to identify the forces. Once you have your forces and where they're acting identified, then you can try to write the relevant equations.
 
  • #3
ais the back of the foot and b is the front with the ball.
 
  • #4
Two questions: (1) Just to make sure, is the heel of the foot off the ground? (2) Do you have the distance between ta and b?
 
  • #5
That was suppose to be "between a and b"
 

Related to Find Tension & Force Exerted by Shinbones on Foot w/ W, a, & b

1. What is the formula for finding tension and force exerted by shinbones on foot?

The formula for finding tension and force exerted by shinbones on foot is T = ma + b, where T is the tension, m is the mass of the person, a is the acceleration of the person, and b is the weight of the person's foot.

2. How do you determine the values for mass, acceleration, and weight in the formula?

Mass can be measured using a scale or by calculating the density and volume of an object. Acceleration can be calculated by measuring the change in velocity over time. Weight can be determined using the formula weight = mass * gravity, where gravity is typically 9.8 m/s^2 on Earth.

3. Can the formula be used for any person's shinbones and foot?

Yes, the formula can be used for any person's shinbones and foot as long as the mass, acceleration, and weight values are accurately measured for that specific person.

4. How does the tension and force exerted by shinbones on foot affect a person's posture and movement?

The tension and force exerted by shinbones on foot play a crucial role in a person's posture and movement. If the tension is too high, it can cause strain and discomfort in the legs and feet. On the other hand, if the tension is too low, it can affect balance and stability.

5. Are there any other factors that can affect the tension and force exerted by shinbones on foot?

Yes, there are other factors that can affect the tension and force exerted by shinbones on foot, such as the person's overall health, muscle strength, and footwear. These factors can impact the accuracy of the formula and should be taken into consideration when calculating tension and force.

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