Problem 1: You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M, length L) 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 xoffsetfrom the end of the board when seated as shown.You have selected a child of mass m (shown on the right), and an adult of mass n times the mass of the child (shown on the left) to test out your prototype. Part (a) Derive an expression for the torque applied by the adult rider (on the left) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive.Expression :τ = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (b) Derive an expression for the torque applied by the child rider (on the right) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive.Expression :τ = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (c) Derive an expression for the torque applied by the board in terms of given quantities and variables available in the palette.Expression :τ = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (d) Determine the distance d in terms of n, g, and the masses and lengths in the problem.Expression :d = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (e) Determine the magnitude of the force exerted on the pivot point by the see-saw while in use in terms of given quantities and variables available in the palette.Expression :Fnet = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffset HIХssetXoffset

Question

Problem 1:  You have been hired to design a family-friendly see-saw. Your design will feature a uniform board (mass M, length L) 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 xoffsetfrom the end of the board when seated as shown.You have selected a child of mass m (shown on the right), and an adult of mass n times the mass of the child (shown on the left) to test out your prototype.    Part (a) Derive an expression for the torque applied by the adult rider (on the left) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive.Expression   :τ = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (b) Derive an expression for the torque applied by the child rider (on the right) in terms of given quantities and variables available in the palette. Assume counterclockwise is positive.Expression   :τ = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (c) Derive an expression for the torque applied by the board in terms of given quantities and variables available in the palette.Expression   :τ = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (d) Determine the distance d in terms of n, g, and the masses and lengths in the problem.Expression   :d = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffsetPart (e) Determine the magnitude of the force exerted on the pivot point by the see-saw while in use in terms of given quantities and variables available in the palette.Expression   :Fnet = __________________________________________Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, h, j, k, L, m, M, n, P, t, xoffset HIХssetXoffset

Accepted Answer

(a)The torque is defined as the product of force and the perpendicular distance. Consider the figure…

HI Хsset Xoffset