The slotted arm oa rotates about a fixed axis through o at...

The slotted arm OA rotates about a fixed axis through O. At the instant under consideration, $\theta = 38^\circ$, $\dot{\theta} = 37$ deg/s, and $\ddot{\theta} = 14$ deg/s$^2$. Determine the magnited of the force F applied by arm OA and the magnitude of the force N applied by the sides of the slot to the 0.3-kg slider B. Neglect all friction, and let L = 0.81 m. The motion occurs in a vertical plane. Answers: F = N N = N

Transcript

00:02 In this problem we have this object with this mass that is moving along this arm and the arm is rotating.

00:14 So the polar coordinates that we use to describe the motion of the object are er component and the theta coordinate.

00:28 So we have some information for this theta component.

00:32 We have its value in the theta coordinate.

00:34 This instance, we also have the first derivative.

00:38 So this first derivative, we can rewrite using radiance over second instead of degrees over second.

00:47 For that, we multiply by pi and divide by 180 degrees.

00:52 So doing that, we have that this is pi over four radiance divided by second.

01:01 And this is pi over nine radiance, per second.

01:09 We want to compute the forces that are applied to this object.

01:20 So we have some forces.

01:23 First, the force from the arm that is perpendicular to the arm.

01:28 So this is that force.

01:31 We are going to call it f .a.

01:34 We also have the force due to the walls of the vertical slot.

01:35 So this is that force.

01:35 This is a force.

01:35 We are going to call it f .a.

01:35 We also have the force due to the walls of the vertical slot.

01:39 So as this is a normal force is perpendicular.

01:44 So it's horizontal and we're going to call it f s.

01:51 And we also have the weight of the particle.

01:55 So the weight is m g.

01:59 So basically this is a free body layer, this part here.

02:05 So in order to compute the values of these forces, we need to use the equations of motion.

02:13 So using polar coordinates the equation of motion are these two equations here.

02:20 So for these two equations we just replace the summation of the forces in these directions and use these expressions for the acceleration.

02:33 So as we need our first derivative of r and second derivative of r, let's use the figure to compute these values.

02:46 So first, for r, from the triangle here, this triangle, we can easily check that this r is l over cosine, theta.

03:02 So from here we can compute the value of r.

03:08 So we just need to take the derivative of this expression...

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