An amusement park has two themed resorts, Stargazer Suites and Retro Retreat. The graph and table below display the cost of the
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9514 1404 393
Answer:
- resultant force: 93.946∠-10.62° N
- line of action: 17.314x +92.337y = 809.433
Step-by-step explanation:
We can use the notation a∠b to represent the (x, y) components (a·cos(b), a·sin(b)), where angle b is measured CCW from the +x direction. If we label the forces a, b, c, d clockwise from A, then we have ...
a = 80∠0° = (80, 0)
b = 60∠90° = (0, 60)
c = 90∠45° = (63.640, 63.640)
d = 150∠-110° = (-51.303, -140.954)
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If we label point A the origin, then the clockwise torque on point A is the sum of products of the force x-component and its y location, and its y-component and the negative of its x location.
T = (0, 0)·(80, 0) +(3, 0)·(0, 60) +(3, -8)·(63.640, 63.640) +(0, -8)·(-51.303, -140.954)
T = 809.433 . . . . n·m, the CW torque on point A
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The sum of forces is ...
F = a +b +c +d = (92.337, -17.314) = 93.946∠-10.62° . . . N
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This force, applied to the point of application, must generate the same torque as the given forces. That is ...
F·(y, -x) = 809.433
Then the equation of the line of action is ...
17.314x +92.337y = 809.433 . . . . . x and y in meters measured from A
Any point (x, y) on this line will serve as a point of application of the force. Unfortunately, this line of action does not pass through the rectangular plate. The attachment shows the point (D) on the line of action that is closest to point A.
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<em>Additional comment</em>
The resultant force could be decomposed into two forces acting <em>on the rectangular plate</em>. One could be of much larger magnitude, operating at the corner opposite point A. This force would provide the necessary torque. Another would be acting on point A, providing no torque, but with components such that the resultant has the correct magnitude and direction.
It takes 42 minutes for 6 people to paint 7 walls
<em><u>Solution:</u></em>
It takes 54 minutes for 4 people to paint 6 walls
To find: Minutes required for 6 people to paint 7 walls
If men can do
work in
days working
hours per day and
men can do
work in
days working
hours per day, then
M = Number of men
D = Number of days
H = Number of hours per day
W = Amount of work
Here in this sum,
<em><u>54 minutes for 4 people to paint 6 walls</u></em>
<em><u>Minutes required for 6 people to paint 7 walls</u></em>
<em><u>Substituting the values in formula, we get</u></em>
Thus it takes 42 minutes for 6 people to paint 7 walls