How would you use the parallelogram method of vector addition when more than two forces are added?
1 answer:
Answer:
In order to use the parallelogram method, we have to select first two vectors. We move the vectors until their initial points coincide. Then we draw lines to form a complete parallelogram, as is shown in the figure annexed. The diagonal from the initial point to the opposite vertex of the parallelogram is the resultant.
We use the last vector resultant with a third vector, and we use again the parallelogram method to add them. We use the new resultant and we add it with a 4th vector. We repeat this task until all the vectors are used.
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Answer: 288.8 m
Explanation:
We have the following data:
is the time it takes to the child to reach the bottom of the slope
is the initial velocity (the child started from rest)
is the angle of the slope
is the length of the slope
Now, the Force exerted on the sled along the ramp is:
(1)
Where is the mass of the sled and
its acceleration
In addition, if we draw a free body diagram of this sled, the force along the ramp will be:
(2)
Where is the acceleration due gravity
Then:
(3)
Finding :
(4)
(5)
(6)
Now, we will use the following kinematic equations to find :
(7)
(8)
Where is the final velocity
Finding from (7):
(9)
(10)
Substituting (10) in (8):
(11)
Finding :