A 4.0g slug moves at a speed of 3.0cm/min. much energy would the slug expend in climbing a plant stalk 16cm high? At what rate would this energy be expended? Finally, if the slug’s muscles are only 18% efficient, how much chemical energy must have been converted in order for the slug to climb the plant?

Question

A 4.0g slug moves at a speed of 3.0cm/min. much energy would the slug expend in climbing a plant stalk 16cm high? At what rate would this energy be expended? Finally, if the slug’s muscles are only 18% efficient, how much chemical energy must have been converted in order for the slug to climb the plant?

Answer 1

work = energy = mgh

time = distance/speed
power = work/time

chemical energy = energy/.18

watch the units

Answer 2

To calculate the energy expended by the slug in climbing the plant stalk, we need to consider the gravitational potential energy gained by the slug. The formula for gravitational potential energy is:

Potential energy = mass * gravity * height

1. First, let's calculate the potential energy gained by the slug:
Mass of the slug (m) = 4.0 grams = 0.004 kg
Gravitational acceleration (g) = 9.8 m/s^2
Height (h) = 16 cm = 0.16 meters

Potential energy (PE) = m * g * h
= 0.004 kg * 9.8 m/s^2 * 0.16 m
= 0.006208 Joules

So, the slug would expend approximately 0.006208 Joules of energy in climbing the plant stalk.

2. To determine the rate at which this energy is expended, we can divide the energy by the time taken. We know that the slug moves at a speed of 3.0 cm/min. So, the time taken (t) can be calculated using the distance traveled (d) and speed (v) using the formula:

Time taken (t) = distance / speed

Distance (d) = height = 16 cm = 0.16 meters
Speed (v) = 3.0 cm/min = 0.05 cm/s

Time taken (t) = 0.16 m / 0.05 m/min
= 3.2 minutes

Now, we can calculate the rate of energy expenditure:

Rate = Energy / Time
= 0.006208 J / 3.2 min
≈ 0.0019 J/min

Therefore, the slug would expend energy at a rate of approximately 0.0019 Joules per minute.

3. Lastly, since the slug's muscles are only 18% efficient, we need to account for this efficiency to determine the amount of chemical energy converted. The efficiency is given as a percentage, so we need to convert it to a decimal form (18% = 0.18). The equation for calculating the amount of chemical energy is:

Chemical energy = Potential energy / Efficiency

Chemical energy = 0.006208 J / 0.18
≈ 0.03449 J

So, approximately 0.03449 Joules of chemical energy must have been converted for the slug to climb the plant stalk.

*How

work = energy = mgh

To calculate the energy expended by the slug in climbing the plant stalk, we need to consider the gravitational potential energy gained by the slug. The formula for gravitational potential energy is: