Find the magnitude and the direction of vactor C=3A - 2B, draw the three vectors in x-y system.
1 answer:
Since we already have the x and y components of vectors A and B, we just need to perform the equation for C in the two components.
x-component:
y-component:
We then solve for the magnitude of vector C by using the pythagorean theorem:
For the direction, if we perform the operation
, we'll get the angle from the horizontal.
ANSWER: Vector C has a magnitude of 24.17 N and a direction of 114.44 degrees from the horizontal.
x-component:
y-component:
We then solve for the magnitude of vector C by using the pythagorean theorem:
For the direction, if we perform the operation
ANSWER: Vector C has a magnitude of 24.17 N and a direction of 114.44 degrees from the horizontal.
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Missing figure and missing details can be found here:
<span>http://d2vlcm61l7u1fs.cloudfront.net/media%2Fdd5%2Fdd5b98eb-b147-41c4-b2c8-ab75a78baf37%2FphpEgdSbC....
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Solution:
(a) The work done by the spring is given by
where k is the elastic constant of the spring and
is the stretch between the initial and final position. Since x1=-8 in=-0.203 m and x2=5 in=0.127 m, we have
(b) The work done by the weight is the product of the component of the weight parallel to the inclined plane and the displacement of the cart:
where the negative sign is given by the fact that
points in the opposite direction of the displacement of the cart, and where
therefore, the work done by the weight is
<span>http://d2vlcm61l7u1fs.cloudfront.net/media%2Fdd5%2Fdd5b98eb-b147-41c4-b2c8-ab75a78baf37%2FphpEgdSbC....
</span>
Solution:
(a) The work done by the spring is given by
where k is the elastic constant of the spring and
(b) The work done by the weight is the product of the component of the weight parallel to the inclined plane and the displacement of the cart:
where the negative sign is given by the fact that
therefore, the work done by the weight is