2. Two adult movers push a box on a frictionless floor as shown with forces of 1
ID: 2137511 • Letter: 2
Question
2. Two adult movers push a box on a frictionless floor as shown with forces of 120.0 N and 173.2 N. Because the box starts to move away from the x-axis, a child decides to exert a third force on the box, and will make the box move in the x-direction only.
(i) Find the SMALLEST magnitude of force the child should apply, to keep the cart moving in the x-direction. (Ignore all other forces, and ignore friction.).
(ii) If the child pushes with the force found in (i), then the cart has an acceleration of +2.0 m/s2 in the x-direction.
How much does the wheeled cart weigh, in N?
Two adult movers push a box on a frictionless floor as shown with forces of 120.0 N and 173.2 N. Because the box starts to move away from the x-axis, a child decides to exert a third force on the box, and will make the box move in the x-direction only. Find the SMALLEST magnitude of force the child should apply, to keep the cart moving in the x-direction. (Ignore all other forces, and ignore friction.). If the child pushes with the force found in (i), then the cart has an acceleration of +2.0 m/s2 in the x-direction. How much does the wheeled cart weigh, in N?Explanation / Answer
t appears that the child puts in enough force to lift the skids of the cart off the ground
Adult 1 is pushing DOWN @ 60 degrees 100N
The vertical component of that push is
sin 60 = Y1/100
Y1 = 86.6 N DOWN ===> - 86.4 N
Adult 2 is pushing UP @ 30 degrees 140 N
Vertical component is
sin 30 = Y2/140
Y2 = 70 N UP ===> +70
Net Force by by the adults is 70 - 86.6 = - 16.6 N
===> Child must put in 16.6 N UP to lift the skids so the cart will move (a)
Now we need the horizontal components of the adults, the child has no horizontal component.
cos 60 = X1/100
X1 = 50 N
cos 30 = X2/140
X2 = 121.24 N
Total: 121.24 + 50 = 171.24 N (Note the X components are both in the + X direction That component lies exactly on the X axis not 5.54 degrees above. Re-check your calculation and think it through again)
F = MA
171.24 N = M * 2 m/s^2
M = 171.24/2 = 85.62 kg
But we need weight
F = MA = 85.62 * 9.8 m/s^2 = 839.09 N
I used more accurate numbers than your book. ===> I got your book answers, if you allow for rounding.
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