asst 20 qanda

course Phy 201

ÄFÉÎD·ÄÆcëòy—¹Þϼ¼¥­ÕãÅassignment #020

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

020. Forces (inclines, friction)

Physics II

11-16-2007

......!!!!!!!!...................................

01:04:11

`q001. Note that this assignment contains 3 questions.

. A 5 kg block rests on a tabletop. A string runs horizontally from the block over a pulley of negligible mass and with negligible friction at the edge of the table. There is a 2 kg block hanging from the string. If there is no friction between the block in the tabletop, what should be the acceleration of the system after its release?

......!!!!!!!!...................................

RESPONSE -->

2kg*9.8m/s^2=19.6kgm/s^2

confidence assessment: 1

.................................................

......!!!!!!!!...................................

01:06:57

Gravity exerts a force of 5 kg * 9.8 meters/second = 49 Newtons on the block, but presumably the tabletop is strong enough to support the block and so exerts exactly enough force, 49 Newtons upward, to support the block. The total of this supporting force and the gravitational force is zero.

The gravitational force of 2 kg * 9.8 meters/second = 19.6 Newtons is not balanced by any force acting on the two mass system, so we have a system of total mass 7 kg subject to a net force of 19.6 Newtons.

The acceleration of this system will therefore be 19.6 Newtons/(7 kg) = 2.8 meters/second ^ 2.

......!!!!!!!!...................................

RESPONSE -->

Gravity exerts 5kg*9.8m/s^2=49N but the table exerts the same force to counteract it for a gravitational force of zero.

The gravitational force of 2kg*9.8m/s^2=19.6N

Total mass=2kg+5kg=7kg

Acceleration of the system= 19.6N/7kg=2.8m/s^2

self critique assessment: 2

.................................................

......!!!!!!!!...................................

01:09:47

`q002. Answer the same question as that of the previous problem, except this time take into account friction between the block in the tabletop, which exerts a force opposed to motion which is .10 times as great as the force between the tabletop and the block. Assume that the system slides in the direction in which it is accelerated by gravity.

......!!!!!!!!...................................

RESPONSE -->

9.8m/s^2*5kg=49N

.1*49N=4.9N

4.9N is in the direction opposite to the motion

19.6N-4.9N=14.7N

divide by 7kg

=2.1m/s^2

confidence assessment: 2

.................................................

......!!!!!!!!...................................

01:10:21

Again the weight of the object is exactly balance by the upward force of the table on the block. This force has a magnitude of 49 Newtons. Thus friction exerts a force of .10 * 49 Newtons = 4.9 Newtons. This force will act in the direction opposite that of the motion of the system. It will therefore be opposed to the 19.6 Newton force exerted by gravity on the 2 kg object.

The net force on the system is therefore 19.6 Newtons -4.9 Newtons = 14.7 Newtons. The system will therefore accelerate at rate a = 14.7 Newtons/(7 kg) = 2.1 meters/second ^ 2.

......!!!!!!!!...................................

RESPONSE -->

a=14.7N/7kg=2.1m/s^2

self critique assessment: 3

.................................................

......!!!!!!!!...................................

01:17:06

`q003. Answer the same question as that of the preceding problem, but this time assume that the 5 kg object is not on a level tabletop but on an incline at an angle of 12 degrees, and with the incline descending in the direction of the pulley.

......!!!!!!!!...................................

RESPONSE -->

Total force= 19.6N on 7kg

incline of 12 degrees

confidence assessment: 0

.................................................

......!!!!!!!!...................................

01:20:51

In this case you should have drawn the incline with the x axis pointing down the incline and the y axis perpendicular to the incline. Thus the x axis is directed 12 degrees below horizontal. As a result the weight vector, rather than being directed along the negative y axis, lies in the fourth quadrant of the coordinate system at an angle of 12 degrees with the negative y axis. So the weight vector makes an angle of 270 degrees + 12 degrees = 282 degrees with the positive x axis.

The weight vector, which has magnitude 5 kg * 9.8 meters/second ^ 2 = 49 Newtons, therefore has x component 49 Newtons * cosine (282 degrees) = 10 Newtons approximately. Its y component is 49 Newtons * sine (282 degrees) = -48 Newtons, approximately.

The incline exerts sufficient force that the net y component of the force on the block is zero. The incline therefore exerts a force of + 48 Newtons. Friction exerts a force which is .10 of this force, or .10 * 48 Newtons = 4.8 Newtons opposed to the direction of motion. Assuming that the direction of motion is down the incline, frictional force is therefore -4.8 Newtons in the x direction.

The weight component in the x direction and the frictional force in this direction therefore total 10 Newtons + (-4.8 Newtons) = + 5.2 Newtons. This force tends to accelerate the system in the same direction as does the weight of the 2 kg mass. This results in a net force of 5.2 Newtons + 19.6 Newtons = 24.8 Newtons on the 7 kg system.

The system therefore accelerates at rate {}

a = (24.8 Newtons) / (7 kg) = 3.5 meters/second ^ 2, approximately.

......!!!!!!!!...................................

RESPONSE -->

Am confused about how to draw the incline.

Also where did the 270 degrees come from to add to 12 degrees

Weight vector=5kg*9.8m/s^2=49N

x component=49N *cosine(282degrees)=10N

y component=49N *sine(282degrees)=-48N

self critique assessment: 2

If the object rests on a level surface then, if the x axis is in the direction of motion it will be parallel to the surface and hence horizontal, directed to the right.

The weight of the object, which is the force exerted on it by gravity, is directed straight down. The weight vector is therefore in the direction of the negative y axis.

The angular position of the negative y axis, as measured counterclockwise from the positive x axis, is 270 degrees (starting from the x axis it requires 90 deg to get to the positive y axis, another 90 deg to get to the negative x axis, and another 90 deg to get to the negative y axis). So the weight vector is at an angle of 270 deg as measured in this coordinate system.

Now if the level surface is tilted 12 degrees in the clockwise direction, the x axis will be pointing at 12 degrees below horizontal, and the y axis will also rotate 12 degrees in the clockwise direction. The weight vector is still directed vertically downward; the y axis has rotated 12 degrees clockwise from the weight vector. This puts the weight vector in the fourth quadrant of the new coordinate system. As measured in this system the weight vector makes an angle of 282 degrees with the positive x axis (starting from the x axis, measuring counterclockwise, it requires 270 deg to get to the negative y axis and another 12 deg to get to the weight vector).

.................................................

&#

Very good responses. Let me know if you have questions. &#