Suppose a 34.5-kg child sits 1.17 m to the left of center on the same seesaw as the problem you just solved in the PRACTICE IT section. A second child sits at the end on the opposite side, and the system is balanced.
a) 34.5/(L/2) x 1.17= weight of second child (kg)
b) weight of second child+34.5 kg+weight of plank (given in part B in the practice it)multiplied by 9.8= N
To solve this problem, we can use the concept of torque. Torque is the product of the force applied and the lever arm distance. In this case, the torque created by each child must be equal for the seesaw to be balanced.
The torque created by the first child can be calculated as follows:
Torque1 = Force1 x Distance1
The torque created by the second child can be calculated as follows:
Torque2 = Force2 x Distance2
Since the seesaw is balanced, we can equate the two torques:
Torque1 = Torque2
Given:
Weight1 = 34.5 kg (weight of the first child)
Distance1 = 1.17 m (distance of the first child from the center)
Distance2 = length of the seesaw (distance of the second child from the center)
Let's assume:
Weight2 = force exerted by the second child
Using the equation above, we have:
Weight1 x Distance1 = Weight2 x Distance2
Substituting the given values into the equation, we have:
34.5 kg x 1.17 m = Weight2 x Distance2
Simplifying the equation:
40.365 kg·m = Weight2 x Distance2
To find the weight of the second child (Weight2), we need to determine the distance of the second child from the center (Distance2).
We can use the fact that the total torque of a balanced system is zero. In this case, the torque created by the first child must be equal in magnitude but opposite in direction to the torque created by the second child.
The torque created by the first child (Torque1) can be calculated as follows:
Torque1 = Weight1 x Distance1
The torque created by the second child (Torque2) can be calculated as follows:
Torque2 = Weight2 x Distance2
Since the seesaw is balanced, we can then write:
Torque1 = -Torque2
Substituting the given values into the equation, we have:
Weight1 x Distance1 = -Weight2 x Distance2
Now we can solve for the distance of the second child from the center (Distance2):
Weight2 x Distance2 = -(Weight1 x Distance1)
Distance2 = -(Weight1 x Distance1) / Weight2
Finally, substitute the given values into the equation to compute the distance:
Distance2 = -(34.5 kg x 1.17 m) / Weight2
To find the weight of the second child (Weight2), we need to use the fact that the total weight on each side of the seesaw must be equal for it to balance:
Weight1 + Weight2 = Total weight
Given:
Weight1 = 34.5 kg (weight of the first child)
Total weight = weight of the second child (Weight2) + weight of the seesaw
Substituting the given values into the equation, we have:
34.5 kg + Weight2 = Weight2 + weight of the seesaw
To solve for the weight of the second child (Weight2), we need to know the weight of the seesaw. However, without that information, we cannot determine the exact value of Weight2 or Distance2.
To solve this problem, we can use the principle of moments or torques. The principle of moments states that for a system to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
Let's assume that the pivot point or fulcrum of the seesaw is located in the center. We'll label the two sides of the seesaw as left and right.
Given:
- Mass of the first child (on the left side): 34.5 kg
- Distance of the first child from the center: 1.17 m
To balance the system, we need to find the mass of the second child and the distance from the center at which they sit. Let's call the mass of the second child M2, and the distance from the center D2.
Since the system is balanced, the total clockwise moments must be equal to the total counterclockwise moments.
Moment due to the first child: (Mass of the first child) * (Distance of the first child from the center)
Clockwise moment = 34.5 kg * 1.17 m
Moment due to the second child: (Mass of the second child) * (Distance of the second child from the center)
Counterclockwise moment = M2 * D2
Equating these two moments:
34.5 kg * 1.17 m = M2 * D2
Now, we need to solve for the mass of the second child (M2).
Given that the system is balanced, the total mass on each side of the seesaw must be equal:
Mass of the first child = Mass of the second child
34.5 kg = M2
Now we can substitute this value back into the equation:
34.5 kg * 1.17 m = M2 * D2
Solve for D2:
D2 = (34.5 kg * 1.17 m) / M2
Substituting the value of M2, we get:
D2 = (34.5 kg * 1.17 m) / 34.5 kg
Simplifying:
D2 = 1.17 m
So, the second child must sit 1.17 m to the right of the center to balance the seesaw with the given conditions.