Answer:
Explanation:
a= 7.8i + 6.6j - 7.1k
b= -2.9 i+ 7.4 j+ 3.9k , and
c = 7.6i + 8.8j + 2.2k
r = a - b +c
=7.8i + 6.6j - 7.1k - ( -2.9i + 7.4j+ 3.9k )+ ( 7.6i + 8.8j + 2.2k)
= 7.8i + 6.6j - 7.1k +2.9i - 7.4j- 3.9k )+ 7.6i + 8.8j + 2.2k
= 18.3 i +18.3 j - k
the angle between r and the positive z axis.
cosθ = 18.3 / √18.3² +18.3² +1
the angle between r and the positive z axis.
= 18.3 / 25.75
cos θ= .71
45 degree
Absolutely ! If you have two vectors with equal magnitudes and opposite
directions, then one of them is the negative of the other. Their correct
vector sum is zero, and that's exactly the magnitude of the resultant vector.
(Think of fifty football players pulling on each end of the rope in a tug-of-war.
Their forces are equal in magnitude but opposite in sign, and the flag that
hangs from the middle of the rope goes nowhere, because the resultant
force on it is zero.)
This gross, messy explanation is completely applicable when you're totaling up
the x-components or the y-components.
Answer: a) The acceletarion is directed to the center on the turntable. b) 5 cm; ac= 0.59 m/s^2; 10 cm, ac=1.20 m/s^2; 14 cm, ac=1.66 m/s^2
Explanation: In order to explain this problem we have to consider teh expression of the centripetal accelartion for a circular movement, which is given by:
ac=ω^2*r where ω and r are the angular speed and teh radios of the circular movement.
w=2*π*f
We know that the turntable is set to 33 1/3 rev/m so
the frequency 33.33/60=0.55 Hz
then w=2*π*0.55=3.45 rad/s
Finally the centripetal acceleration at differents radii results equal:
r= 0.05 m ac=3.45^2*0.05=0.50 m/s^2
r=0.1 ac=3.45^2*0.1=1.20 m/s^2
r=0.14 ac=3.45^2*0.14=1.66 m/s^2
Answer:
static coefficient = 0,203 & kinetic coefficient = 0,14
Explanation:
There are two (2) conditions, when the desk is about to move and when the desk is moving. In the attachements you can see the two free body diagram for each condition.
In the first condition, there is no movement and the force is 12 N, in the image we can see the total forces are equal to 0 and by the definition of the friction force we can get the static friction coefficient.
In the second condition there is movement in the direction of the force which is equal to 8 N, again by the definition of the friction force we can get the kinetic friction coefficient. Since the desk is moving with constant velocity there is not acceleration.
