NOTE: The value of r_ddot provided should be r_ddot = 40 m/s2, not 3 m/s2. Apologies for the typo.
Discussion and hints:
Note that most of the Given information is in terms of a polar description of kinematics: r, r_dot, r_ddot, θ and θ_dot. Consider using a set of polar coordinates for both your kinetics and kinematics.
Recall the following four-step plan outline in the lecture book and discussed in lecture:
Step 1: FBDs
Draw a free body diagram for particle P. Recall that the force in a spring is the stiffness k times the amount of stretch in the spring, Δ, where Δ = spring length – unstretched spring length.
Step 2: Kinetics (Newton’s 2nd Law)
Write down the r – and θ -components of the Newton’s 2nd law equations for the particle.
Step 3: Kinematics
Write down the polar description for the acceleration of the particle.
Step 4: Solve
From your kinetics and kinematics equations, solve for the unstretched length of the spring.
Any questions??