A 450.8 N child and a 101.0 N child sit on either end of a 2.2 m long seesaw.

How far from the 450.8 N child should the pivot be placed to ensure rotational equilibrium? Disregard the mass of the seesaw. Answer in units of m
part 2 of 2
Suppose a 367 N child sits 0.193 m from the 450.8 N child. How far from the pivot must a 261 N child sit to maintain rotational equilibrium? Answer in units of m

The torques have be equaled

P1x=P2(2.2-x)
x=(P2•2.2)/( P1+ P2)=0.4 m
Part 2
P1•0.4+P3(0.4-0.193) = P2•1.8+P4•x, P4
where P1=450.8 N, P2=101.0 N, P3= 367 N, and P4=261 N.
Calculate x

Where did you get the 1.8 from

To ensure rotational equilibrium in a seesaw, the torques on both sides of the pivot must be equal.

For part 1:
Let's assume the distance from the pivot to the 450.8 N child is x.

The torque exerted by the 450.8 N child is given by:
Torque1 = Force1 * Distance1
= 450.8 N * x

The torque exerted by the 101.0 N child is given by:
Torque2 = Force2 * Distance2
= 101.0 N * (2.2 m - x)

For rotational equilibrium, Torque1 must be equal to Torque2:
450.8 N * x = 101.0 N * (2.2 m - x)

Let's solve this equation for x:
450.8x = 222.2 - 101.0x
551.8x = 222.2
x ≈ 0.402 m

Therefore, the pivot should be placed approximately 0.402 m from the 450.8 N child to ensure rotational equilibrium.

For part 2:
Let's assume the distance from the pivot to the 261 N child is y.

The torque exerted by the 450.8 N child is still given by:
Torque1 = 450.8 N * x

The torque exerted by the 367 N child is given by:
Torque2 = Force2 * Distance2
= 367 N * (0.193 m - x)

The torque exerted by the 261 N child is given by:
Torque3 = Force3 * Distance3
= 261 N * (y)

For rotational equilibrium, the sum of the torques must be zero:
Torque1 + Torque2 + Torque3 = 0
450.8 N * x + 367 N * (0.193 m - x) + 261 N * y = 0

Let's substitute the value of x we found in part 1 (0.402 m) into the equation:
450.8 N * 0.402 m + 367 N * (0.193 m - 0.402 m) + 261 N * y = 0

Simplifying the equation:
180.9608 N + 367 N * (-0.209 m) + 261 N * y = 0
-76.9033 N + 261 N * y = 0
261 N * y = 76.9033 N
y = 76.9033 N / 261 N
y ≈ 0.295 m

Therefore, the 261 N child must sit approximately 0.295 m from the pivot to maintain rotational equilibrium.

To ensure rotational equilibrium in the first scenario, we can use the principle of moments. The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments about a pivot point must be equal to the sum of the counterclockwise moments about the same pivot point.

In this case, we have two children sitting on the seesaw. Let's call the distance from the pivot to the 450.8 N child x. The distance from the pivot to the 101.0 N child is given as 2.2 m - x (since the total length of the seesaw is 2.2 m).

Now, we can set up the equation for rotational equilibrium:

Moment(clockwise) = Moment(counterclockwise)

Let's calculate the moments for each child:

Moment(clockwise) = (450.8 N) * x
Moment(counterclockwise) = (101.0 N) * (2.2 m - x)

Setting these two moments equal to each other, we get:

(450.8 N) * x = (101.0 N) * (2.2 m - x)

Simplifying the equation, we have:

450.8x = 222.2 - 101x

Combining like terms:

551.8x = 222.2

Dividing both sides by 551.8:

x = 0.402 m

Therefore, the pivot should be placed approximately 0.402 m from the 450.8 N child to ensure rotational equilibrium in the first scenario.

Now, let's move on to the second scenario.

In this scenario, we have a 367 N child sitting 0.193 m from the 450.8 N child. We need to find the distance from the pivot that a 261 N child should sit to maintain rotational equilibrium.

We can apply the same principle of moments to this scenario. Let's call the distance from the pivot to the 261 N child y.

Using the same approach as before, we can set up the equation for rotational equilibrium:

Moment(clockwise) = Moment(counterclockwise)

The moment for the 367 N child is given by:

Moment(clockwise) = (367 N) * (0.193 m - x)

And the moment for the 261 N child is:

Moment(counterclockwise) = (261 N) * y

Setting these two moments equal to each other:

(367 N) * (0.193 m - x) = (261 N) * y

Simplifying the equation:

70.831 N - 367x = 261y

Dividing by 261:

0.271 m - 1.406x = y

Therefore, the distance from the pivot that the 261 N child should sit to maintain rotational equilibrium is approximately 0.271 m - 1.406x.