High-speed motion pictures (3500frames/second) of a jumping 280ìg flea yielded the data to plot the flea's acceleration as a function of time as shown in the figure (Figure 1). This flea was about 2 mm long and jumped at a nearly vertical takeoff angle. Find the initial net external force on the flea. How does it compare to the flea's weight? Find the maximum external net force on this jumping flea. When does this maximum force occur?
To find the initial net external force on the flea, we need to determine the area under the acceleration curve shown in Figure 1. The area under the curve represents the change in velocity of the flea, which, in turn, can be related to the net external force acting on it.
Here's how you can calculate the initial net external force:
1. Determine the mass of the flea:
Given that the mass of the flea is 280 μg (micrograms), we need to convert it to kilograms.
280 μg = 280 × 10^(-9) kg = 2.8 × 10^(-7) kg
2. Calculate the change in velocity:
The change in velocity can be determined by finding the area under the acceleration curve. Since the acceleration is given as a function of time, we need to integrate the acceleration over time to find the change in velocity.
3. Approximate the change in velocity graphically:
If you have access to the graph of acceleration versus time, estimate the change in velocity by measuring the area under the curve. Use appropriate units for time and acceleration.
4. Calculate the initial net external force:
The initial net external force can be calculated using Newton's second law of motion, F = m * a, where F is the net external force, m is the mass of the flea, and a is the change in velocity.
Once you have determined the initial net external force, you can compare it to the weight of the flea to understand how they relate. If the initial net external force is greater than the weight of the flea, it means there are additional external forces acting on the flea during its jump.
To find the maximum external net force on the jumping flea and when it occurs:
1. Analyze the acceleration versus time graph:
Observe the acceleration versus time graph and identify the point where the acceleration reaches its maximum (peak) value.
2. Calculate the maximum external net force:
Using Newton's second law, F = m * a, where F is the external net force, m is the mass of the flea, and a is the maximum acceleration.
3. Determine when the maximum force occurs:
The time at which the maximum force occurs can be read from the graph or can be determined by considering the time corresponding to the peak of the acceleration curve.
By following these steps, you can find the initial net external force on the flea, compare it to the flea's weight, and also determine the maximum external net force and when it occurs during the flea's jump.