Discussion and hints:

Since all motion is in a horizontal plane and with the contact surface of the slot with P being smooth, the speed of P will remain constant throughout. And, with the speed being a constant, there will be only a normal (centripetal) component of acceleration for P. (If you do not see this from the beginning, no worries. Your analysis will show you this.) This is seen in the animation provided below.

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 for the position of interest: x = 0. Please be reminded that the motion of the system is in a horizontal plane. With this and with the slot being smooth, only the normal contact force from the slot acts on P.

Step 2: Kinetics (Newton’s 2nd Law)
Write down the t – and n -components of the Newton’s 2nd law equations for P.

Step 3: Kinematics
Here, we will consider the constrained motion of particle P. Use the chain rule to determine y_dot in terms of x_dot, as well as y_ddot in terms of x_ddot. For the instant of interest, i = e_t and j = e_n.

Step 4: Solve
From your kinetics and kinematics equations, solve for the normal contact force, N.

Any questions??