First, what is the speed of the block and cylinder after you have pulled the blo

Question

First, what is the speed of the block and cylinder after you have pulled the block and cylinder 52 cm down the plane?

How far have you pulled the block and cylinder when everything stops?

You pull on a string with a horizontal force F = 34 N that is attached to a block of mass mb = 7.1 kg, then to the axle of a solid cylinder of mass mc = 5.7 kg and radius r = 0.4 m, then to a spring of spring constant k = 115 N/m. This is all done on an inclined plane where there is friction ( Us = 0.6 and First, what is the speed of the block and cylinder after you have pulled the block and cylinder 52 cm down the plane? How far have you pulled the block and cylinder when everything stops? Theta = 25 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. Mu k = 0.30 ), and the incline angle is

Explanation / Answer

First, draw a diagram to help you visualize what's happening, and that will give you a framework for writing down all the forces acting in the system.

Then do an analysis using conservation of energy: Basically, you have work (= energy) begin done by the force pulling the string; you have frictional losses; you have kinetic energy of the system as well as the loss of potential energy by its lowering the heights of the block and the cylinder. Having done the energy balancing (using equations), you'll then know which forces you need expressions for.

Then, go through each object and figure out all the forces acting on it (and that you need for your energy conservation equation). Each one has gravity (except the spring, maybe), and there are other forces as well; and the block and the cylinder are both losing potential energy as they descend.

The block has a horizontal force from the string; you have to resolve this force into its components, one parallel and one perpendicular to the incline plane. The one parallel acts together with the component of gravity in the same direction pulling the block down the hill. The one perpendicular to the plane acts to reduce the normal force of gravity insofar as that determines the frictional force on the block, which always acts opposite to its direction of motion.

Then you have the two frictional forces to consider, the one depending on the static and the other on the kinetic coefficients of friction.

IOW, the block has a lot of things going on!

The cylinder is simpler, because you're not given a coefficient of rolling friction, so you don't have to include that. But you have both angular (rotational) and translational (movement down the incline) motion to remember to consider. Again, as with the block, gravity is acting to pull the cylinder down the incline, as is the connection to the block. Don't forget to use torque and the moment of inertia I when it comes to the rolling motion of the cylinder.

Then you have the spring. Assume it is fixed at the other end and is massless. It doesn't have any gravitational forces on it directly; it has the force stretching it parallel to the incline, and that force is constantly changing as it becomes more stretched (F = -k * x).

I hope this has helped you analyze the kinematics of the situation. I assume you know all the equations to use in applying your analysis to calculate the answers wanted!

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