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?
please help me this is badly needed. i need to pass this tomorrow. im hoping for your response.
M1*d1 = M2*d2.
M1*1.2 = M2*1.5, M1 = 1.25M2.
(M1+14)*1.8 = M2*3.
(1.25M2+14)1.8 = 3M2,
2.25M2 + 25.2 = 3M2, M2 = 33.6 kg, F2 = M2*g = 33.6*9.8 = 329.3 N. = Wt. of the girl.
M1 = 1.25M2 = 1.25*33.6 = 42 kg,
F1 = 42*9.8 = 411.6 N. = Wt. of the boy.
To solve this problem, we'll consider the concept of torques or moments of force. Torque is the turning force or rotational force caused by a force acting at a distance from a pivot point.
Let's denote the weight of the boy as Wb and the weight of the girl as Wg. We need to find the values of Wb and Wg.
We can start by considering the balanced scenario where the boy is sitting 1.20 meters from the center. In this case, the girl sits 1.50 meters from the center.
The torque for the boy is calculated by multiplying the weight of the boy by the distance from the center: Torqueb = Wb * 1.20
Similarly, the torque for the girl is calculated as Torqueg = Wg * 1.50
Since the seesaw is balanced, the torques on both sides must be equal:
Torqueb = Torqueg
Using the information given, we can set up the equation: Wb * 1.20 = Wg * 1.50
Now, let's consider the scenario where the boy carries an additional mass of 14 kg and sits 1.80 meters from the center. In this case, the girl must move to 3 meters from the center to balance it.
Using the same logic as before, we can calculate the new torques:
Torqueb = (Wb + 14) * 1.80
Torqueg = Wg * 3
Again, the torques must be equal for the seesaw to be balanced:
Torqueb = Torqueg
Substituting the values into the equation, we have: (Wb + 14) * 1.80 = Wg * 3
Now we have two equations:
1.20Wb = 1.50Wg
1.80(Wb + 14) = 3Wg
Solving this system of equations will give us the values of Wb and Wg.
Here's how you can proceed to solve for Wb and Wg:
1. Solve equation 1.20Wb = 1.50Wg for Wb:
Divide both sides by 1.20:
Wb = (1.50Wg) / 1.20
2. Substitute this value of Wb into equation 1.80(Wb + 14) = 3Wg:
1.80((1.50Wg) / 1.20 + 14) = 3Wg
3. Simplify and solve for Wg:
Multiply 1.80 by the expression inside the parentheses: (1.80 * 1.50Wg) / 1.20 + (1.80 * 14) = 3Wg
4. Simplify further and solve for Wg:
(2.70Wg / 1.20) + (25.20 / 1.20) = 3Wg
5. Combine like terms and isolate Wg:
2.25Wg + 21 = 3Wg
6. Subtract 2.25Wg from both sides and isolate Wg:
21 = 0.75Wg
7. Divide both sides by 0.75:
Wg = 21 / 0.75
8. Calculate Wg to find the weight of the girl.
9. Substitute this value of Wg back into the equation Wb = (1.50Wg) / 1.20 to calculate the weight of the boy, Wb.
By solving these equations, you'll be able to find the weights of the boy and the girl. Make sure to double-check your calculations for accuracy.