A 83.2-kg man stands on his toes by exerting an upward force through the Achilles tendon, as in the figure below. What is the force in the Achilles tendon if he stands on one foot?
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To determine the force in the Achilles tendon when a man stands on one foot, we need to consider the forces acting on his body.
Let's break down the problem step by step:
Step 1: Identify the forces acting on the man.
When the man is standing on one foot, the only two forces acting on him are:
1. The force of gravity pulling him downward, which we can calculate as weight = mass x acceleration due to gravity. In this case, weight = 83.2 kg x 9.8 m/s^2.
2. The force exerted by the Achilles tendon to counteract the force of gravity.
Step 2: Calculate the force of gravity.
By multiplying the mass of the man (83.2 kg) by the acceleration due to gravity (9.8 m/s^2), we can find the force of gravity: weight = 83.2 kg x 9.8 m/s^2.
Step 3: Determine the force in the Achilles tendon.
Since the man is standing, the force in the Achilles tendon must be equal in magnitude and opposite in direction to the force of gravity. Therefore, the force in the Achilles tendon is equal to the force of gravity calculated in Step 2.
Step 4: Calculate the force in the Achilles tendon.
Plugging in the calculated value of weight into the equation from Step 3, we find that the force in the Achilles tendon is equal to the weight of the man, which is 83.2 kg x 9.8 m/s^2.
So, the force in the Achilles tendon when the man stands on one foot is 815.36 Newtons.