Worksheet
Calculating Force Components
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When working with vectors, it is often necessary to resolve a vector into its component parts. To introduce this technique, we are going to use as our reference frame the rectangular grid of the x|y plane common to students from their work in Algebra I and Algebra II.
When we speak of a "diagonal force vector" we mean a vector which points towards the interior of a quadrant, not one that lies along the x- or y-axis.
Much of what we are going to discuss goes back to former lessons on
properties of vectors
and
basic trigonometry
.
Note that no matter into which "quadrant" your vector points, angle
ϴ
should always next to the x-axis, it is called the reference angle.
As you will see in some of the following examples, if the given angle is not in standard position then you can always use geometry to find the angle next to the nearest x-axis. Alternatively, the component called "cosine" is always adjacent to whichever angle is given and the second component is always called "sine."
Refer to the following information for the next nine questions.
Determine the horizontal and vertical components of each tension shown in the following situation.
What is the magnitude of the horizontal component of the 50-N force?
In which direction is this horizontal component directed?
+x
+y
-x
-y
What is the magnitude of the horizontal component of the 64-N force?
In which direction is this horizontal component directed?
+x
+y
-x
-y
What is the magnitude of the vertical component of the 50-N force?
In which direction is this vertical component directed?
+x
+y
-x
-y
What is the magnitude of the vertical component of the 64-N force?
In which direction is this vertical component directed?
+x
+y
-x
-y
Are all of the forces acting on the block balanced?
no
yes
cannot be determined
Refer to the following information for the next fourteen questions.
Consider an object which has been placed in equilibrium by three concurrent force vectors.
The following measurements have been taken:
vector 1 had a spring scale reading of 17 N at 42º cw from the negative x-axis
vector 2 had a spring scale reading of 20 N at 75º ccw from the positive y-axis
vector 3 had a spring scale reading of 18 N at 22º cw from the negative y-axis
What is the magnitude of the horizontal component of vector 1?
In which direction is this horizontal component directed?
+x
+y
-x
-y
What is the magnitude of the horizontal component vector 2?
In which direction is this horizontal component directed?
+x
+y
-x
-y
What is the magnitude of the horizontal component vector 3?
In which direction is this horizontal component directed?
+x
+y
-x
-y
According to your calculations, is the object in equilibrium horizontally? That is, is net F
_{x}
= 0?
absolutely not
more or less
cannot be determined
What is the magnitude of the vertical component vector 1?
In which direction is this vertical component directed?
+x
+y
-x
-y
What is the magnitude of the vertical component of vector 2?
In which direction is this vertical component directed?
+x
+y
-x
-y
What is the magnitude of the vertical component of vector 3?
In which direction is this vertical component directed?
+x
+y
-x
-y
Are all of the vertical forces acting on the object balanced?
absolutely not
more or less
cannot be determined
Refer to the following information for the next six questions.
Consider a passenger pulling a 12-kg suitcase down a concourse at a constant velocity of 1 m/sec.
If the passenger is exerting a 75-N force along the handle at a 53º angle, then what is the magnitude of the force's horizontal component?
What is the magnitude of the vertical component of the 75-N force?
How much does the suitcase weigh?
What is the magnitude of static friction acting against the suitcase's wheels?
What is the net force normal acting on the suitcase by the floor?
What is the coefficient of static friction?
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