A force 1 of magnitude 7.20 units acts on an object at the origin in a direction θ = 29.0° above the positive x-axis. (See the figure below.) A second force 2 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 1 + 2.
Well, if I were to graphically represent this situation, it would probably look like a bunch of arrows pointing in different directions. Let me grab a pen and paper and draw it for you. Okay, here we go:
/\ Force 1 (7.20 units)
/ \
/ \
/ \
/ \
________/________\_______
Force 2 (5.00 units)
Now, let's find the resultant force by adding the two forces together. To do this graphically, we can use the good ol' head-to-tail method.
- First, draw the tail of the second force at the head of the first force (force 1).
- Then, draw the resultant force from the tail of the first force to the head of the second force.
If you can imagine it, the resultant force will be the diagonal side of a triangle formed by the two forces. So, let's find that magnitude and direction!
To find the magnitude, we can measure the length of the resultant force using a ruler. I'm going to eyeball it here... hmm... it looks like it's about 9.0 units.
Now, to find the direction of the resultant force, we need to measure the angle it makes with the positive x-axis. Ah, there it is... it looks like about 61.0°.
So, the magnitude of the resultant force is approximately 9.0 units and its direction is approximately 61.0° above the positive x-axis.
And there you have it! The graphical representation of the magnitude and direction of the resultant force 1 + 2. I hope that helps!
To find the magnitude and direction of the resultant force 1 + 2, we can use vector addition.
Step 1: Draw a coordinate system with the x-axis extending to the right and the y-axis extending upwards. Mark the origin (0,0) where the object is located.
Step 2: Draw force 1 with a length of 7.20 units at an angle of 29.0° above the positive x-axis. Draw force 2 with a length of 5.00 units in the direction of the positive y-axis.
Step 3: To find the resultant force, place the tail of force 2 at the head of force 1. This means that the tail of force 2 should be at the point where force 1 ends.
Step 4: Draw the vector that starts from the origin and ends at the head of force 2. This is the resultant force 1 + 2.
Step 5: Measure the length of the resultant force using a ruler. The length is the magnitude of the resultant force.
Step 6: Measure the angle that the resultant force makes with the positive x-axis. This angle is the direction of the resultant force.
Step 7: Report the magnitude and direction of the resultant force.
Note: The procedure described above is a graphical method for finding the magnitude and direction of a vector. It should be noted that this method is not as accurate as using trigonometric calculations. If precise calculations are required, the use of trigonometry is recommended.
To find the magnitude and direction of the resultant force, we can use the graphical method of vector addition. Here are the steps to get the answer:
1. Draw a coordinate system with x and y axes.
2. Draw a vector for force 1 of magnitude 7.20 units, making an angle of 29.0° above the positive x-axis.
3. Draw a vector for force 2 of magnitude 5.00 units, pointing in the direction of the positive y-axis.
4. To find the resultant vector, add the two vectors together by placing the tail of the second vector at the head of the first vector.
5. Draw a vector from the tail of the first vector to the head of the second vector. This is the resultant vector.
6. Measure the magnitude of the resultant vector using a ruler or a scale.
7. Measure the angle the resultant vector makes with the positive x-axis using a protractor.
By following these steps, you will be able to graphically determine the magnitude and direction of the resultant force.