Really hard problem...?

Question

A wedge of mass m = 35.5 kg is located on a plane that is inclined by an angle θ = 21.7 with respect to the horizontal. A force F = 349.3 N in horizontal direction pushes on the wedge, as shown. The coefficient of friction between the wedge and the plane is 0.143.

What is the acceleration of m along the plane? Negative numbers for motion to the left, and positive numbers for motion to the right, please.

I've tried so many different approaches, and I just can't get it... Please help, and try to explain how you got it, if possible. Because I'm lost. Thanks!

Answer 1

Okay, so you have to draw a free bodied diagram, and it has to be very careful. Some hints:

Tilt the x-y axes of your system so that the x-axis lies parallel to the incline surface and the y-axis points normal to it. This will make the components of the weight look weird (as well as the applied force) but it makes it easier to analyze the acceleration as well as the frictional force. The applied force will have to be resolved according to the angle at which it is applied to the wedge in the system that you have set up.

In short, if it doesn't point along the x or y axis, try resolving it into components along the x or y axis using available angles (theta will be used for the weight, and the other angle for the applied force).

From this set up your force equations. Because of the tilt of our new coordinate system, you will only have acceleration along the new x-axis (in other words the wedge isn't accelerating off the incline).

My last word of advice is a repeat. Draw the freebodied diagram *very* carefully, and the equations should follow directly. Mind the angles.

Good luck, and if you need more help, I'll keep an eye on the problem.

Answer 2

Since I don;t have the figure that you refer to, I can't give you an exact answer, but here's the process.

This is a force vector problem. You need to break the forces into their vector components which I am presuming that you know generally how to do.

Establish a coordinate system with the x axis parallel to the angled plane, and the y axis perpendicular to the plane.

Now, you need to break all the forces down into components along these axes. Why did I choose these axes? Because for a block on an inclined plane, only the force parallel to the surface of the plane makes the block move. Forces perpendicular to the plane's surface cause the block to push into the plane, but don't contriibute to its motion.

For example, gravity points straight down. The vector component of it parallel to the plane would be W * sin(a) and the vecotor component perpendicular to the plane would be W*cos(a), where W is the weight of the block and a is the angle. You can test this by setting the angle a = 0 and you should see that the vertical component equals the weight and the horizontal = 0.

Once you decompose the weight of the block into its two vector components, do the same thing for the force F. Since the force is horizontal, it also needs to be split into two vector components, again, one perpindicular to the surface of the inclined plane, and the other component parallel to it.

You now have four force components, (2 from W and 2 from F).
Add the two components that are parallel to the plane. This gives you the net force pushing the block across the plane. Call this Fnet_parallel.

Add the two components that are perpendicular to the surface of the inclined plane. This is the total force that is causing the block to push into the plane. Call this Fnet_perp. Now, multiply this force Fnet_perp. by the coefficient of friction (0.143) to calculate the resistive force.

Since this resistive force acts in a direction opposite to Fnet_parallel, subtract it from Fnet_parallel. This is the net force that causes the block to move. Since you know the force, and you know the mass of the wedge (35.5kg) you can calculate the acceleration from F = MA... Rearrange it to calculate A = F/M.

Hope this helps.. its a long answer but the concept isn't too difficult. The trick with all problems like this is to figure out how to orient the coordinate system, in this case one axis parallel, and one perpendicular to the surface of the inclined plane.

Have fun..

Answer 3

The shape being a wedge may be throwing you. This doesn't actually matter, substitute a point mass sliding down the plane. The force should be divided into vectors. The horizontal component given by Fcos(where'd you find a theta key?) and the vertical component by Fsin(theta). This should give you a good starting point.