Question

There is a species of Darwin’s finch on the Galapagos Islands that can exert a force of 205 N with its beak as it cracks open a seed case. If its beak moves through a distance of 0.40 cm during this operation, how much work does the finch do to get at the seed inside the case?

Short answer

The finch does 0.82 J of work.

Step-by-step solution

Understanding Work Formula

The formula to calculate work is given by \[ \text{Work} = \text{Force} \times \text{Distance} \]. Here, the force exerted by the finch's beak is 205 N, and the distance is 0.40 cm, which needs to be converted to meters for standard SI units.

Converting Distance to Meters

Since the distance needs to be in meters, convert 0.40 cm to meters:\[ 0.40 \text{ cm} = 0.40 \div 100 = 0.004 \text{ m} \].

Calculate Work Done

Substitute the given values into the work formula:\[ \text{Work} = 205 \text{ N} \times 0.004 \text{ m} \]. Calculate the multiplication to find the work done by the finch.

Final Calculation

Perform the final calculation:\[ \text{Work} = 205 \times 0.004 = 0.82 \] J. Thus, the finch does 0.82 Joules of work.

Key concepts

Force and Motion

Force and motion go hand in hand when discussing concepts in physics. A force is a push or pull exerted on an object, leading to motion or a change in motion. In our exercise, the force is applied by the finch's beak as it presses against the seed case. Here, force is measured in newtons (N), which is the standard unit. The value 205 N indicates how strongly the finch applies its beak to crack the seed case. Motion, on the other hand, refers to the change in position of an object. When force is applied, motion generally occurs unless counteracted by an equal force. In this scenario, the finch’s beak moves through a specified distance of 0.40 cm. This movement is essential to calculate the work done by the finch's effort. Understanding the relationship between force and motion helps us make calculations related to work, a concept arising whenever a force causes an object to move a certain distance.

Calculation of Work

Work is a fundamental concept in physics, linking force, motion, and energy together. It describes the energy transferred to or from an object via the application of force along a displacement. The formula for calculating work is:

• \[ \text{Work} = \text{Force} \times \text{Distance} \]

This equation implies that work is the product of the force applied to an object and the distance over which the force is applied. The result is expressed in joules (J), where one joule equates to the energy expended when applying a force of one newton over a distance of one meter.In the exercise, substituting the values we have:

• Force = 205 N
• Distance = 0.004 m (after conversion)

Put these into the equation:

• \[ \text{Work} = 205 \times 0.004 = 0.82 \] J

Thus, the finch performs 0.82 joules of work while cracking open the seed case.

SI Units Conversion

In physics, calculations are typically performed using the International System of Units (SI) for consistency and accuracy. It ensures that equations balance correctly and results are universally understandable. In the exercise, the distance moved by the finch’s beak is given in centimeters (cm). Since the work formula requires distance in meters (the SI unit for distance), a conversion is necessary. Converting units maintains accuracy in calculations:

• To convert cm to m, divide by 100 since 1 m = 100 cm. Thus,
• 0.40 cm becomes 0.40/100 = 0.004 m

Performing such conversions allows us to apply the work formula correctly without errors arising from inconsistent units. Always use SI units when engaging in scientific calculations to ensure precision and transparency.