A 0.350 kg birdie is being hit between two badminton players. The graphs show the birdie's velocity and the force exerted on the birdie by the badminton racket. If the birdie is in contact with the racket for Δt=5.40 ms, what is the maximum force exerted on the birdie?
force*time=massbirdie(change in velocity)
you can solve for force. Remember change in velocity is vf-vi, and at impact, the birdie travels in opposite direction (v has a change of sign)
To find the maximum force exerted on the birdie, we need to find the area under the force exerted vs. time graph during the time interval Δt.
Given information:
Mass of the birdie (m) = 0.350 kg
Time interval (Δt) = 5.40 ms = 5.40 × 10^-3 s
We'll use the equation for force (F) in terms of mass (m) and acceleration (a):
F = m * a
From the force vs. time graph, we can see that the force exerted on the birdie is not constant but changes during the interval Δt.
To estimate the maximum force exerted, we'll calculate the average force over the time interval Δt. Using the formula for average force, which is equal to the change in momentum divided by the change in time:
Average force (F_avg) = Δp / Δt
The change in momentum (Δp) can be calculated using the formula:
Δp = m * Δv
To find Δv, we need to determine the change in velocity of the birdie during the time interval Δt. We can estimate this by finding the area under the velocity vs. time graph during the same time interval.
From the velocity vs. time graph, we can see that the velocity of the birdie changes from a positive value to a negative value over the time interval Δt.
To calculate the change in velocity (Δv), we can split the area under the graph into two triangles and find the areas of both triangles separately, then sum them up:
Area of Triangle 1 = (1/2) * base1 * height1
Area of Triangle 2 = (1/2) * base2 * height2
The base1 and height1 correspond to the time and velocity at the beginning of Δt, while base2 and height2 correspond to the time and velocity at the end of Δt.
Finally, we can calculate the average force (F_avg) by dividing the change in momentum by Δt.
Average force (F_avg) = Δp / Δt
Maximum force = F_avg
By following these steps, we can find the maximum force exerted on the birdie.
To find the maximum force exerted on the birdie, we need to analyze the graph of the force exerted on the birdie by the racket.
1. Look at the graph: The graph represents the force exerted on the birdie by the racket. The force is measured in Newtons (N) and the time is measured in milliseconds (ms).
2. Identify the peak: Find the point on the graph where the force is at its maximum value. This will be the highest point on the graph.
3. Read the value: Once you have found the peak, read the value of the force from the vertical axis. This will give you the maximum force exerted on the birdie.
4. Note the units: Make sure to take note of the units of the force you have obtained. In this case, it should be in Newtons (N).
By following these steps, you should be able to determine the maximum force exerted on the birdie. If you provide additional information (such as a description of the graph), I can help you further with the calculations.