26 Query

course Phy 201

7/15 12:20AM

026. `query 26

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Question: `qgen phy and principles of phy 4.36: If the coefficient of kinetic friction is .30, how much force is required to push a 35 kg crate across the floor at constant speed?

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Your solution:

The friction will be .30(normal force)

Fn=35kg(9.8m/s/s)=343N.

Therefore friction will be .30(343N) or -102.9N.

We want the acceleration to be equal to 0 for the object to be at a constant speed. Since F=m(a), we need force to also equal 0. This means that 102.9N of force must be applied for the object to move at a constant speed.

Confidence rating: 2

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Given Solution:

`aIf the crate is moving then the force exerted by friction is .30 times the normal force between it and the floor. If the push is horizontal, then the only horizontal forces acting on the crate are the downward force of gravity and the upward force exerted by the floor. Since the crate is not accelerating in the vertical direction, these forces are equal and opposite so the normal force is equal to the weight of the crate.

The weight of the crate is 35 kg * 9.8 m/s^2 = 340 N, approx.

The frictional force is therefore

f = .30 * 340 N = 100 N, approx..

If the crate moves at constant speed, then its acceleration is zero, so the net force acting on it is zero.

The floor exerts its normal force upward, which counters the gravitational force (i.e., the weight).

The frictional force acts in the direction opposite motion; if net force is zero an equal and opposite force is required, so you must push the box with a force of 100 N in the direction of motion.

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Self-critique (if necessary):

OK

Self-critique Rating: OK

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Question: `qgen phy 4.55 18 kg box down 37 deg incline from rest, accel .27 m/s^2. what is the friction force and the coefficient of friction?

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Your solution:

F=mass(acc)

F=18kg(.27m/s/s) which is 4.86N

We then need to use our vector diagram to find the normal force and the gravitational force parallel to the incline.

Parallel will be Wcos(37) or 140.9N

140.9-(106*x)=4.86N

Friction is 1.28N.

This means the coeff is 1.28/4.86 or .27

Confidence rating:

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Given Solution:

`aGOOD STUDENT SOLUTION: (I don't know why, but I was hoping you would pick an odd numbered problem here)Here goes.....For an 18kg box on an incline of 37 degrees with an acceleration of .270 m/s/s, I first drew out a diagram showing the forces involved. Next the forces had to be derived.

First, to find the force associated with the weight component parrallel to the inline moving the box downward....Fp=sin 37 deg(18kg)(9.8m/s/s)=106N.

Next, the Normal force that is counter acting the mg of the box is found by..

Fn=cos 37 deg. (18kg)(9.8 m/s/s) = 141N.

The frictional force can be found by using F=(mass)(acceleration) where (Net Force)-(frictional coeffecient*Normal Force)=(m)(a) so that...

106N - (141N * Friction Coeff.) = (18kg)(.270 m/s/s) where by rearranging, the frictional coeffecient is seen to be .717.

INSTRUCTOR COMMENT:

Good solution.

Note that you should specify an x axis oriented down the incline, so that the acceleration will be positive.

The weight vector being vertical in the downward direction is therefore in the fourth quadrant, at an angle of 37 degrees with respect to the negative y axis.

Thus the weight vector makes angle 270 deg + 37 deg = 307 deg with the positive x axis and its x and y components are

wtx = 18 kg * 9.8 m/s^2 * cos(307 deg) = 106 N and

wty = 18 kg * 9.8 m/s^2 * sin(307 deg) = -141 N.

You get the same results using the sin and cos of the 37 deg angle.

The only other y force is the normal force and since the mass does not accelerate in the y direction we have normal force + (-141 N) = 0, which tells us that the normal force is 141 N.

This also agrees with your result. **

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Self-critique (if necessary):

I keep getting this confused. Would the x component be sin(theta) or cos(theta)

I thought it was cos, but here they use sin for the parr gravity

I've revised the solution in the original document for this Open Query in response to your question, which is a very common point of confusion.

The key idea is that the circular-model definitions lead us to an x-y coordinate system in which the weight vector is at angle 307 degrees relative to the positive x axis, while the right-triangle analysis can be done in terms of a triangle containing the 37-degree incline. The sine of one angle is the cosine of the other, and vice versa, except for + and - signs.

The + and - signs arise naturally from the circular model, which is the advantage of this model.

The triangular model also has its advantages.

The explanation includes some figures, which can't be represented in this response. So see the original document for much more.

Self-critique Rating:

3

&#This looks good. See my notes. Let me know if you have any questions. &#