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Chapter 7: Problem 51

Biology During mating season, male bighorn sheep establish dominance with head-butting contests which can be heard up to a mile away. When two males butt heads, the "winner" is the one that knocks the other backward. In one contest a sheep of a mass \(95 \mathrm{~kg}\) and moving at \(10 \mathrm{~m} / \mathrm{s}\) runs directly into a sheep of mass \(80 \mathrm{~kg}\) moving at \(12 \mathrm{~m} / \mathrm{s}\). Which ram wins the head-butting contest? SSM

Short Answer

Expert verified
The ram with mass 80 kg and moving at 12 m/s wins the head-butting contest as it has a larger momentum of 960 kg m/s compared to the 950 kg m/s of the other ram.

Step by step solution

01

Calculate the momentum of first sheep

For the first sheep with mass \(95 kg\) and velocity \(10 m/s\), calculate momentum as \(p_1 = m_1 \cdot v_1 = 95 kg \cdot 10 m/s = 950 kg \cdot m/s\).
02

Calculate the momentum of second sheep

For the second sheep with mass \(80 kg\) and velocity \(12 m/s\), calculate momentum as \(p_2 = m_2 \cdot v_2 = 80 kg \cdot 12 m/s = 960 kg \cdot m/s\).
03

Compare the momentums

Compare the momentums of both sheep. The sheep with the larger momentum should be able to knock back the other sheep. As \(p_2 > p_1\), the second sheep should win the head-butting contest.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Momentum Calculation
Momentum is a key concept in physics that helps us understand motion and collisions. It combines an object's mass and velocity to gauge how much force it can exert or withstand in a collision. Here鈥檚 how momentum is calculated:

\[ p = m \cdot v \]

where \( p \) is momentum, \( m \) is mass, and \( v \) is velocity. In the context of two rams clashing, each animal鈥檚 momentum determines its impact force. To calculate, simply multiply the mass of the ram by its velocity. This allows us to see which ram has a stronger force moving in, and thus, which one might prevail in their head-to-head battle.
Collision Dynamics
Collision dynamics delve into what happens when objects, like our two rams, collide. The principle of conservation of momentum tells us that the total momentum before the collision equals the total momentum after. In simpler terms, all the momentum the rams bring into the crash remains the same afterward, though it might be redistributed.

When two rams butt heads, their momentums act against each other. If a ram has more momentum, it can knock the other one backward. By comparing their momentums, we realize that the ram with the greater momentum (960 kg路m/s vs. 950 kg路m/s) will typically come out as the winner of this vigorous contest.
Animal Biomechanics
Animal biomechanics examines how animals move and exert force. It applies principles like momentum to real-world biological processes. In the head-butting of bighorn sheep, biomechanics explains not only why one ram wins but also how their bodies withstand the tremendous forces.

These sheep have specially designed skulls and neck muscles that act like shock absorbers. This adaptation helps them survive and dominate during these contests. Understanding biomechanics helps us appreciate how animals are naturally equipped to handle forces that would otherwise be harmful.

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Most popular questions from this chapter

An open rail car of initial mass \(10,000 \mathrm{~kg}\) is moving at \(5 \mathrm{~m} / \mathrm{s}\) when rocks begin to fall into it from a conveyor belt. The rate at which the mass of rocks increases is \(500 \mathrm{~kg} / \mathrm{s}\). Find the speed of the train car after rocks have fallen into the car for a total of \(3 \mathrm{~s}\).

A 2-kg ball is moving at \(3 \mathrm{~m} / \mathrm{s}\) toward the right. It collides elastically with a 4-kg ball that is initially at rest. Determine the velocities of the balls after the collision.

In a game of pool, the cue ball is rolling at \(2 \mathrm{~m} / \mathrm{s}\) in a direction \(30^{\circ}\) north of east when it collides with the eight ball (initially at rest). The mass of the cue ball is \(170 \mathrm{~g}\) but the mass of the eight ball is only \(156 \mathrm{~g}\). After the completely elastic collision, the cue ball heads off \(10^{\circ}\) north of east and the eight ball moves off due north. Find the final speeds of each ball after the collision.

A sudden gust of wind exerts a force of \(20 \mathrm{~N}\) for \(1.2 \mathrm{~s}\) on a bird that had been flying at \(5 \mathrm{~m} / \mathrm{s}\). As a result, the bird ends up moving in the opposite direction at \(7 \mathrm{~m} / \mathrm{s}\). What is the mass of the bird?

An object is traveling in the positive \(x\) direction with speed \(v\). A second object that has half the mass of the first is traveling in the opposite direction with the same speed. The two experience a completely inelastic collision. The final \(x\) component of the velocity is A. 0 B. \(v / 2\) C.v/3 D. \(2 v / 3\) E. \(v\)
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