A force
F1
of magnitude 6.90 units acts on an object at the origin in a direction 𝜃 = 55.0° above the positive x-axis. (See the figure below.) A second force
F2
of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force
F1 + F2.
magnitude _________ units
direction _________ ° counterclockwise from the +x-axis
can someone explain it step by step like I was in the first grade?
F1x = 6.90 cos55.0°
F1y = 6.90 sin55.0°
F2x = 0
F2y = 5.00
So, if F = F1+F2 then
Fx = F1x + F2x
Fy = F1y + F2y
|F| = √(Fx^2 + Fy^2)
at an angle θ such that
tanθ = Fy/Fx
This should all look familiar ...
F1,
x component = 6.9 cos 55 = 3.96
y component = 6.9 sin 55 = 5.65
F2
x component = 5.0 cos 90 = 0
y component = 5.0 sin 90 = 5.00
Resultant = F
F
x component = 3.96 + 0 = 3.96
y component = 5.65 + 5.00 = 10.65
magnitude = |F| = sqrt (10.65^2+5^2) = 11.77
tan theta = 10.65/3.96 = 2.69
theta = 69.6 degrees above x axis
Sure! Let's break it down step by step:
Step 1: Start by drawing a coordinate system where the positive x-axis is horizontal and the positive y-axis is vertical.
Step 2: Draw a vector F1 of magnitude 6.90 units at the origin. To do this, draw a line segment starting from the origin and make it 6.90 units long inclined 55.0° above the positive x-axis.
Step 3: Draw a vector F2 of magnitude 5.00 units in the direction of the positive y-axis. To do this, draw a line segment starting from the point where F1 ends (the tip of F1) and make it 5.00 units long going straight up along the y-axis.
Step 4: To find the resultant force F1 + F2, simply connect the tail of the first vector (F1) to the tip of the second vector (F2).
Step 5: Measure the magnitude of the resultant force F1 + F2 by measuring the length of the line segment connecting the tail of F1 to the tip of F2. Write down the magnitude.
Step 6: Measure the direction of the resultant force F1 + F2 by measuring the angle it makes counterclockwise from the positive x-axis. Write down the direction.
That's it! You have found the magnitude and direction of the resultant force F1 + F2.