when one boy is sitting 1.20 meter from the center of he seesaw the girl must sit on the other side 1.50 meter from the center to maintain an even balance . however the boy carries an additional mass pf 14 kg and sit 1.80 meter from the center the girl must move to 3 meter from the center to balance . neglecting the weight of the seesaw find the weight of the boy and the girl?

Question

when one boy is sitting 1.20 meter from the center of he seesaw the girl must sit on the other side 1.50 meter from the center to maintain an even balance . however the boy carries an additional mass pf 14 kg and sit 1.80 meter from the center the girl must move to 3 meter from the center to balance . neglecting the weight of the seesaw find the weight of the boy and the girl?

Answer 1

Basic law of playground-math:

the product of the distance and mass on both sides of the teeter-totter must be the same.

so let the boys mass be b kg
and that of the girls be g kg
1.2b = 1.5g
2.4b = 3g

1.8(b+14) = 3g
1.8b + 25.2 = 2.4b
25.2 = .6b
b = 25.2/.6 = 42

sub into 1.2b = 1.5g
1.2(42) = 1.5g
g = 50.4/1.5 = 33.6

state the conclusion by using my definitions

check:
is 1.2(42) = 1.5(33.6) ? yes!
is 1.8(42+14) = 3(33.6) ? Yes!

Answer 2

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Answer 3

To solve this problem, we can use the principle of moments. Moments are calculated by multiplying the weight of an object by its distance from a pivot point.

First, let's set up an equation for when the seesaw is balanced without the additional mass:

Moment of Boy = Moment of Girl

This can be written as:

Weight of Boy * Distance of Boy from Center = Weight of Girl * Distance of Girl from Center

Now let's substitute the given values:

Weight of Boy * 1.20m = Weight of Girl * 1.50m

Now we can solve for the weight of the girl:

Weight of Girl = (Weight of Boy * 1.20m) / 1.50m

Next, let's set up the equation for when the boy carries an additional mass and sits 1.80m from the center:

Moment of Boy + Moment of Additional Mass = Moment of Girl

Weight of Boy * 1.80m + Weight of Additional Mass * 1.80m = Weight of Girl * 3m

Since the additional mass is given as 14kg, we can substitute the value:

Weight of Boy * 1.80m + 14kg * 1.80m = Weight of Girl * 3m

Now we can solve for the weight of the boy:

Weight of Boy = (Weight of Girl * 3m - 14kg * 1.80m) / 1.80m

Using these equations, we can determine the weights of the boy and the girl, given the distances from the center of the seesaw and the additional mass carried by the boy.

Answer 4

To find the weight of the boy and the girl in this scenario, we can use the concept of torque. Torque is the product of the force and the lever arm, which is the perpendicular distance from the force to the axis of rotation.

Let's start by defining a few variables:
- Let "M" be the mass of the girl.
- Let "m" be the mass of the boy.
- Let "d1" be the initial distance of the boy from the center of the seesaw (1.20 meters).
- Let "d2" be the initial distance of the girl from the center of the seesaw (1.50 meters).
- Let "d3" be the final distance of the boy from the center of the seesaw (1.80 meters).
- Let "d4" be the final distance of the girl from the center of the seesaw (3.0 meters).

Now, let's set up equations using the principle of torque balance:

Torque on the left side of the seesaw (initial balance):
m * g * d1 = M * g * d2 -- Equation 1

Torque on the left side of the seesaw (final balance):
(m + 14) * g * d3 = M * g * d4 -- Equation 2

Here, "g" is the acceleration due to gravity (approximately 9.8 m/s²).

From Equation 1, we can rewrite it as:
m * d1 = M * d2 -- Equation 3

Now, by dividing Equation 2 by Equation 3, we can eliminate the term "g":
(m + 14) * d3 / d1 = d4 / d2

Simplifying further, we get:
(m + 14) * d3 * d2 = d4 * d1

Now, we have two equations with two unknowns: m and M. We can solve them simultaneously to find the values of m and M.

Please provide the values of d1, d2, d3, and d4 so that we can proceed with finding the weights of the boy and the girl.