(20%) Problem 5: You have been hired to design a...

(20%) Problem 5: You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 5 kg, length L = 3.7 m) that can be moved so that the pivot is a distance d from the center of the board. This will allow riders to achieve static equilibrium even if they are of different mass, as most people are. You have decided that each rider will be positioned so that his/her center of mass will be a distance x_offset = 13 cm from the end of the board when seated as shown. You have selected a child of mass m1 = 29 kg (shown on the right), and an adult of mass m2 = 89 kg (shown on the left) to test out your prototype. 50% Part (a) Determine the distance d in meters. 50% Part (b) Determine the magnitude of the force exerted on the pivot point by the see-saw while in use in newtons.

Transcript

00:01 All right, so we have a seesaw like this with a fulcrum placed sort of favoring the left side.

00:07 And we're told it's a distance d from the center of the seesaw.

00:12 Let me rewrite that.

00:14 And there is another person at a distance that called xo, like x offset, placed on this part of the seesaw, like this.

00:24 And then we have another person set at the same distance from the right end, we'll call this x not.

00:33 And we want to determine this distance if the mass of this person on the left, let's see, is, let's see, sorry.

00:45 The mass of the person on the right is 29 kilograms.

00:49 The mass of the person on the right is 100, or on the left, excuse me, is 145 kilograms.

00:53 It's five times the mass of the person on the right.

00:56 And the board itself also has a mass of 11 kilograms and has a length of 11 meters.

01:05 And so we first wanted to determine this distance d from the center of the board.

01:11 So let's look at the torques involved in this problem.

01:15 And let's measure our torques relative to the pivot point here where the fulcrum is.

01:22 So under this convention, distances that are to the left of the fulcrum will get a minus sign.

01:27 Distances to the right will get a plus sign.

01:30 And so our torque is going to be our net torque is going to be some of all the torques involved.

01:35 So let's take the torque of the person on the left.

01:39 So their distance is going to be from the pivot point anyway.

01:45 It'll be their mass, which is 145 kilograms, times the acceleration due to gravity.

01:50 I'm going to leave the g in here rather than writing it explicitly because it's actually going to cancel out in our later calculations.

01:56 So that times their distance to the pivot point.

01:59 So if their distance from the center of the board is l over 2...

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