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Answer :
Final answer:
The ratio of the force exerted by a 67 kg person running and striking the ground with a force of 2300N, when compared to the weight of the person, is approximately equal to 3.5.
Explanation:
To find the ratio of the force exerted by a 67 kg person running and striking the ground with a force of 2300N, we first need to determine the person's weight. This can be done using the formula F = m*g, where F is the force (weight of the body), m is the mass of the body (67 kg in this case) and g is the acceleration due to gravity (9.8 m/s²). Therefore, F = 67 kg * 9.8 m/s² = 656.6 N.Now, to find the ratio of the force exerted on the ground to the person's weight, we divide the two forces: R = 2300 N / 656.6 N. The ratio of the force exerted on each foot as it strikes the ground to the force exerted on the ground due to the person's weight is approximately equal to 3.5.
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The force exerted on each foot when running is approximately 3.5 times the body weight of the person.
Determine the weight of the person:
The weight (W) of a person is given by the formula:
[tex]W = m \cdot g[/tex]
where:
- [tex]m[/tex] is the mass of the person (67 kg)
- [tex]g[/tex] is the acceleration due to gravity (approximately 9.8 m/s²)
Plugging in the values, we get:
[tex]W = 67 \text{ kg} \cdot 9.8 \text{ m/s}^2 = 656.6 \text{ N}[/tex]
Given the force exerted on each foot while running:
The force exerted on each foot is [tex]2300 \text{ N}[/tex].
Calculate the ratio of the force exerted to the weight of the person:
The ratio (R) can be found by dividing the force exerted on each foot by the weight of the person:
[tex]R = \frac{F_{foot}}{W}[/tex]
Plugging in the values:
[tex]R = \frac{2300 \text{ N}}{656.6 \text{ N}} \approx 3.5[/tex]
