Help With Physics Assignment: Determining Maximum Velocity & Spring Constant

[g4wonhyo]

Hi, I am taking a physics class with one instructor and the physics lab with another instructor--it wasn't supposed to be that way, and my lab teacher is always giving me a hard time because of it ( I think he hates me.).

Anyway, I need some help with a take-home lab assignment that my lab instructor gave to me. In class, one end of a bungee cord was tied to the railing of the third floor and the other end was tied to a stuffed bear (.176 kg). The bear was dropped from the third floor so that it just barely touched the bottom of the first floor (10.0m). The length of the un-stretched cord was 4.00m, and the length of the stretched cord was 6.00m. I have to determine the maximum velocity and the spring constant. I'm not exactly sure which one I have to calculate first--I think I need the spring constant before I can calculate the maximum velocity (Am I right about that?). To determine the spring constant (k), can I divide the weight of the bear by the displacement of the cord from its un-stretched length?

k=W/x
=.176 kg (9.80 m/s^2)/(6.00m-4.00m)
=.862 N/m

Is that right? Thanks for your help.

 

[M98Ranger]

Hello! It sounds like you are having a difficult time with your physics lab instructor. It's important to remember that your lab instructor is there to help you learn and understand the concepts, so don't be afraid to ask for clarification or additional guidance if needed.

To determine the maximum velocity, you will need to use the conservation of energy equation: PE + KE = constant. PE (potential energy) is equal to the weight of the bear (mgh), where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height the bear was dropped from (10.0 m). KE (kinetic energy) is equal to (1/2)mv^2, where m is the mass and v is the velocity. Since the bear is just barely touching the bottom of the first floor, its potential energy at that point is equal to its kinetic energy. This means that mgh = (1/2)mv^2. You can solve for v to get the maximum velocity.

As for the spring constant, you are correct in thinking that you will need it to calculate the maximum velocity. To determine the spring constant, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position (F = -kx). In this case, the force is the weight of the bear, and x is the displacement of the cord from its un-stretched length (4.00 m). So, you can rearrange the equation to solve for k: k = -F/x. Just make sure to use the negative value of the weight of the bear, since the force is acting in the opposite direction of the displacement.

Your calculation for the spring constant looks correct, but just be sure to include the negative sign in front of the weight of the bear to get a negative value for the spring constant.

I hope this helps and good luck with your lab assignment! Remember to always ask for help if you need it.