Answer:
Explanation:
Here, spring constant is (k) and the inclination angle of the surface is θ
The initial and final positions of the double wheel are considered. Then change in gravitational potential energy, change in kinetic energy, and the change in elastic potential energy of spring are calculated.
Calculate the change in total kinetic energy
Here, mass of the double wheel is m
velocity of the wheel is v
mass moment of inertia of the wheel is I
angular velocity of the wheel is ω
the radius of gyration of the wheel is k
Substitute 10kg for m, 0.125 for k and 0.2 for r
Determine the inclination of the surface with horizontal.
Calculate the change in gravitational potential energy
Here, acceleration due to gravity is g
and the displacement of wheel in horizontal direction is x
Substitute 10kg for m, 9.81m/s² for g, 11.31° for θ
The angle rotated by the wheel α to move x distance is obtained as
Calculate the stretch in the spring
substitute x/200 for α
Calculate the final stretch in the spring.
substitute 1.375x for s
Calculate the change in the elastic potential energy of the spring
Substitute 600N/m for k, 0.225 for x₁ and (0.225 - 1.375x) for x₂
Write the conservation of energy equation for the initial and final positions of the wheel.
Substitute 6.953v² for ΔT, 19.23x for ΔV and (567.18x² - 185.62x) for ΔV_e
..........(1)
Calculate the value of x for which maximum velocity is obtained by differentiating
Differentiate Equation (1) with respect to x.
Substitute 0 for dv/dx
Substitute 0.1467 m in Equation (1)
The maximum velocity of the wheel’s center O is 1.325 m/s