Problem 13 Why can a squirrel jump from a t... [FREE SOLUTION]

Chapter 12: Problem 13

Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?

Short Answer

Expert verified

A squirrel can safely jump from a tree branch to the ground due to its lighter body mass, the buffering effect of air resistance (which affects it more than a human due to its small size), and its anatomical adaptations that help absorb impact, such as a more flexible skeletal structure and stronger leg muscles relative to body size. In contrast, a human could break a bone in a similar fall due to a greater mass, a less significant effect of air resistance, and skeletal and muscular differences that make it harder to absorb the impact.

Step by step solution

Understand the concepts of gravitational potential energy and kinetic energy

Gravitational potential energy (U) is the energy an object possesses due to its height above the ground and is given by the formula U=mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the object relative to the ground. When an object falls, its gravitational potential energy is transformed into kinetic energy (K), which is the energy an object has due to its motion and is given by the formula K = (1/2)mv^2, where m is the mass of the object and v is its velocity.

Calculate the force of impact upon landing

When an object hits the ground, its kinetic energy is transferred into the force of impact. This force is given by the equation F=ma, where F is the force, m is the mass of the object, and a is the acceleration (or deceleration, in this case, when the object comes to a stop). To find the acceleration, use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (0 in this case, as the object is initially at rest), a is the acceleration, and s is the distance fallen (equal to the height of the tree branch).

Factor in the role of air resistance

Air resistance plays a role in reducing the impact of the fall, as it opposes the downward motion of the object. This means that for lighter and smaller objects like squirrels, air resistance has a more significant effect in decreasing their falling speed compared to heavier and larger objects like humans. Consequently, squirrels experience a smaller force of impact when they land compared to humans.

Examine anatomical differences

Squirrels have a lower body mass compared to humans, which reduces the overall force of impact when they land. In addition, squirrels have a more flexible skeletal structure and stronger leg muscles relative to their body size, which allows them to better absorb the impact of the landing.

Conclusion

Overall, a squirrel can jump from a tree branch to the ground and run away undamaged due to a combination of factors, including its lighter body mass, the role of air resistance, and its anatomical adaptations for absorbing impact. On the other hand, a human could potentially break a bone in a similar fall due to a greater mass, a less significant role of air resistance, and differences in the structure of the human skeleton and muscles.

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Why can a squirrel jump from a tree branch to the ground and run away undamaged, while a human could break a bone in such a fall?

Short Answer

Step by step solution

Understand the concepts of gravitational potential energy and kinetic energy

Calculate the force of impact upon landing

Factor in the role of air resistance

Examine anatomical differences

Conclusion

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