Torque and Conservation of energy

Question

Sketch a 0.5 meter wrench, and apply two diagonal forces (which produce torque) to it. Please use two decimal places for the magnitude of each force, and while the torques can each be either clockwise or counter clockwise, the forces must be diagonal (with respect to the wrench). Do not design this problem such that the net torque is zero!

[2] Imagine that the wrench from the previous problem is 20kg. (a) Calculate the moment of inertia of the wrench, by using the equation listed here (for a wrench, use 1/3*M*R^2) (b) Now, using the rotational 1D kinematics equations, calculate how many radians (and rotations) it would travel after 60 seconds of these torques being applied (pretend that the torques remain constant, and that it started from rest).

[3] (a) Think up a conservation of energy problem, and sketch the arena. There must be at least one spring (you choose the spring constant), and you can use that to either give the object an initial potential energy (which is to be converted to speed/motion), or you can have it be compressed at the end of the object’s journey (then you would calculate the “delta x” required for the object to stop). There must be two ramps, one upward and one downward, and if you include a few meters of friction (with kinetic friction coefficient 0.15), that will count as extra credit. (b) Calculate the objects speed after each part (ramp, friction, etc.).

[4] (a) Finish designing the following equilibrium problem (and please do a quick sketch so that the reader can follow!): Have the first person sitting on the left side of a balance beam. (b) Then, have someone pull diagonally on the balance beam, at any location (you decide the magnitude of the force, use two decimal places, and not at the center). (c) Calculate where a 75 kg person would need to sit, if the first person (100 kg) sat 4 meters to the left of the balance beam’s axis. (d) Also calculate the force (in the “x” and “y”) that the support/stand would need to provide (the balance beam is 200 kg, so don’t forget about that “y” force), such that equilibrium is had.

Answer 1

Hello, thank you for taking the time to post your question!

If you want to go over the breakdown of how to draw these in more detail, feel free to shoot me a message and we could set up a lesson! In the online learning studio we would have access to a Whiteboard that will make it much easier to draw.

For a general idea of what it might look like on this first question though, essentially you can think of the wrench as being like a line segment. Then the diagonal forces would be drawn as arrows originating from a point on that line segment. The exact angles and magnitudes of those will have a large impact on what type of torque is present.

Hopefully that gets you moving in the right direction! Feel free to reach out with a message if you have any questions beyond that! :)