Question

You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M = 5 kg, length L = 2.1 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 xoffset = 11 cm from the end of the board when seated as shown. You have selected a child of mass m1 = 28 kg (shown on the right), and an adult of mass m2 = 77 kg (shown on the left) to test out your prototype.

Answer 1

To maintain balance on a seesaw, the clockwise and counterclockwise torques must be equal. In this case, the small child has a mass of 20 kg and the large child has a mass of 30 kg. Given that the total length of the seesaw is 3 m, and the children are separated by a distance of 3 m, we can calculate the distance from the small child to the pivot.

Step-by-step explanation:

To maintain balance on a seesaw, the clockwise and counterclockwise torques must be equal. In this case, the small child has a mass of 20 kg and the large child has a mass of 30 kg. The distance from the small child to the pivot is represented by d1, and the distance from the large child to the pivot is represented by d2. Given that the total length of the seesaw is 3 m, and the children are separated by a distance of 3 m, we can set up the equation:

(20 kg)(d1) = (30 kg)(3 m - d1)

Simplifying the equation, we find that d1 = 1 m.

Answer 2

To balance a seesaw with children of different masses, the torques on either side of the pivot must be equal. The smaller child of mass 20.0 kg must sit 1.80 m from the pivot point to balance a seesaw with another child of mass 30.0 kg, given they are separated by a distance of 3.00 m.

Step-by-step explanation:

Understanding Seesaw Balance and Torque

When designing a seesaw to achieve static equilibrium with riders of different masses, the concept of torque comes into play. Torque, which is the force that causes rotation, depends on both the force applied and the distance from the pivot point at which it is applied. To balance a seesaw, the torques on either side of the pivot must be equal. If we have two children with masses of 20.0 kg and 30.0 kg sitting balanced on a seesaw with the pivot at the center, and they are separated by a distance of 3.00 m, we can use the formula for torque (τ = r × F) to find the distance from the pivot point at which the smaller child must sit.

For equilibrium, the torques must satisfy the following equation:

(20.0 kg × 9.81 m/s2 × d1) = (30.0 kg × 9.81 m/s2 × (3 m - d1))

Let's calculate the distance d1 for the smaller child:

20.0 kg × 9.81 m/s2 × d1 = 30.0 kg × 9.81 m/s2 × (3 m - d1)

Solving for d1, we find:

d1 = (30.0 kg × 3 m) / (20.0 kg + 30.0 kg) = 1.80 m

Therefore, the smaller child must sit 1.80 m from the pivot point to maintain balance on the seesaw.a