Two 20-g flatworms climb over a very thin wall, 10 cm high. one of the worms is20 cm long the other is wider and only 10 cm long. Which of them has done more work against gravity when half of it is over the top of the wall? What is the ratio of the amounts of work done by the two worms?

To determine which flatworm has done more work against gravity while climbing over the wall, we need to consider the concept of work in physics. Work is defined as the force applied to an object times the distance over which that force is applied. In this case, the force is the weight of each worm, and the distance is the height of the wall they are climbing over.

Understanding the Forces Involved

The weight of each worm can be calculated using the formula:

Weight (Force) = mass × gravity

Since both worms are flatworms with the same density, we can infer that their mass is proportional to their volume. The volume of a flatworm can be approximated by considering its length, width, and height. Given that both worms are 20 g, we can directly use their weights in our calculations.

Calculating Work Done

The work done against gravity when climbing over the wall can be expressed as:

Work = Weight × Height

Here, the height of the wall is 10 cm (or 0.1 m). Let's calculate the work done by each worm when half of its body is over the wall.

• Worm 1 (20 cm long, 20 g):
• Weight = 20 g = 0.02 kg
• Work done = 0.02 kg × 9.81 m/s² × 0.1 m = 0.01962 J
• Worm 2 (10 cm long, wider, 20 g):
• Weight = 20 g = 0.02 kg
• Work done = 0.02 kg × 9.81 m/s² × 0.1 m = 0.01962 J

Analyzing the Results

Both worms have the same weight and are climbing the same height, so the work done against gravity is identical for both worms. Therefore, the work done by each worm is:

Work done by Worm 1 = Work done by Worm 2 = 0.01962 J

Determining the Ratio of Work Done

Since both worms have done the same amount of work, the ratio of the work done by Worm 1 to Worm 2 is:

Ratio = Work done by Worm 1 / Work done by Worm 2 = 0.01962 J / 0.01962 J = 1

Final Thoughts

In summary, both flatworms have exerted the same amount of work against gravity while climbing over the wall, resulting in a work ratio of 1:1. This demonstrates that when considering weight and height, the physical dimensions of the worms do not affect the work done in this scenario, as long as their weights remain constant.