1) Determine the extension of the trampoline when a 200 kg person stands on the trampoline. (k=12000)
2) If on the first push, the trampoline went 8.0 cm below its position in part 1, find the average force exerted by his leg muscles?
For the first question i was able to get 0.33m (i think that's the answer, i used mgx=1/2kx^2)
but i have no idea how to do the second question...
1. wrong equation.
Hookes law: force=mg=kx
2. force*distance=1/2 kx^2
Now really, think on that, it gives you half the force on part 1. But because force is linear, from zero to max, it makes sense that the average force then is half the max force, kx.
Avg force=1/2 kx
Okay, so I understand how to do the first question now, but i'm still not clear on how you did the second one...
work going into trampolene= avg force*distance= avgF*x
that equals the stored enrgy 1/2 kx^2
avgF=1/2 kx
To find the average force exerted by the leg muscles in the second question, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the extension or compression of the spring. In this case, the trampoline acts like a spring.
Let's break down the steps to solve the second question:
Step 1: Calculate the extension of the trampoline in meters.
As you mentioned, you obtained the extension of the trampoline in the first question as 0.33 m.
Step 2: Convert the extension from centimeters to meters.
Since the extension was given in centimeters in the question, we need to convert it to meters by dividing it by 100. So, 8.0 cm becomes 0.08 m.
Step 3: Find the average force.
Now that we have the extension, we can calculate the average force exerted by the leg muscles using Hooke's Law: F = k * x.
F represents the force, k is the spring constant, and x is the extension.
In this case:
- The spring constant (k) is given as 12,000 N/m.
- The extension (x) is 0.08 m.
So, the average force exerted by the leg muscles can be found by multiplying the spring constant and extension: F = 12,000 * 0.08.
Simplifying this calculation, the average force is 960 N. Hence, the average force exerted by the leg muscles is 960 Newtons.
Note: Make sure to use consistent units throughout the calculation to avoid errors. In this case, it's important to convert centimeters to meters before performing the calculation.