#$&*
Phy 231
Your 'cq_1_17.2' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A 5 kg cart rests on an incline which makes an angle of 30 degrees with the horizontal.
Sketch this situation with the incline rising as you move to the right and the cart on the incline. Include an x-y coordinate system with
the origin centered on the cart, with the x axis directed up and to the right in the direction parallel to the incline.
The gravitational force on the cart acts vertically downward, and therefore has nonzero components parallel and perpendicular to the
incline.
Sketch the x and y components of the force, as estimate the magnitude of each component.
What angle does the gravitational force make with the positive x axis, as measured counterclockwise from the positive x axis? Which is
greater in magnitude, the x or the y component of the gravitational force?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
Weight of the cart is 5kg*9.8m/s^2=49N.
As measured from the positive x-axis, downward force of gravity makes a 240-degree angle as measured counterclockwise (90 degrees for each quadrant above the x-axis, plus 60 degrees in the -x, -y quadrant.
The y-component of gravity is greater than the x-component at this angle. I estimate visually that the y-component is 45N and the x-component is 25N.
#$&*
Using the definitions of the sine and cosine, find the components of the cart's weight parallel and perpendicular to the incline.
answer/question/discussion: ->->->->->->->->->->->-> scussion:
sin(30deg)=F_x/49N
.5*49N=F_x
The x-component of gravity is 24.5N.
cos(30deg)=F_y/49N
.87*49N=F_y
The y-component of gravity is 42.4N.
#$&*
@&
Good, but the x and y components of the gravitational force are both negative, both directed opposite the positive direction of the corresponding axis.
Using the rule that the cosine gives you the x comonent and the sine gives you the y component, which applies when the angle is measured counterclockwise from the positive x axis, you get
x component = 49 N cos(240 deg) = -24.5 N
y component = 49 N sin(240 deg) = -42 N, approx..
When you use the circular definition and get the angles right, the signs take care of themselves.
Both circular trigonometry and right-angle trigonometry have their advantages. Be sure you're aware of the advantages of both.
*@
How much elastic or compressive force must the incline exert to support the cart, and what is the direction of this force?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
To support the cart without breaking, the incline must exert a force against the y-component of gravity, so the incline must exert 42.4N on the cart.
#$&*
If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> scussion:
If no other force is exerted parallel to the incline, the cart will be subject to that 24.5N force downhill (the x-direction on our axis). 5kg*a=24.5N
Acceleration = 4.9m/s^2.
#$&*
*#&!
&#Good responses. See my notes and let me know if you have questions. &#