Two forces act on a crate as shown
80N / 60N
Draw a vector diagram to show the two forces and calculate the resultant force
the resultant is just the diagonal of the parallelogram with the two vectors as adjacent sides.
To draw the vector diagram, follow these steps:
1. Draw a straight line to represent the crate.
2. Label one end of the line with an arrow pointing upwards, indicating the 80N force.
3. Label the other end of the line with an arrow pointing upwards and slightly to the right, indicating the 60N force.
4. Connect the tail of the 60N arrow with the head of the 80N arrow.
5. Draw a straight line from the tail of the 80N arrow to the head of the 60N arrow.
6. Label this line as the resultant force (R).
To calculate the resultant force, use the Pythagorean theorem:
R = √(80^2 + 60^2)
R = √(6400 + 3600)
R = √10000
R ≈ 100N
Therefore, the resultant force is approximately 100N.
To draw a vector diagram showing the two forces and calculate the resultant force, follow these steps:
1. Begin by drawing a horizontal line to represent the ground or any reference line.
2. Choose a starting point on the line. This point will represent the initial position of the crate.
3. Use an arrow to represent the first force vector. The length of the arrow should be proportional to the magnitude of the force. In this case, the first force is 80N, so you can choose a suitable scale and draw the arrow accordingly. Label the arrow with "80N" to indicate the magnitude and direction of the force.
4. Starting from the tail of the first force arrow, draw a second arrow to represent the second force vector. Again, use a length proportional to the magnitude of the force. The second force is 60N, so draw the arrow accordingly. Label it with "60N" to indicate the magnitude and direction of the force.
5. Once the two arrows are drawn, connect the tail of the first force arrow to the head of the second force arrow with a straight line. This line represents the resultant force.
6. Measure the length of the resultant force line and calculate its magnitude using the same scale you used to draw the arrows. Label the line with the calculated magnitude.
Finally, to calculate the resultant force, use the Pythagorean theorem since the two forces are acting perpendicular to each other. The Pythagorean equation is:
Resultant force magnitude = √(80^2 + 60^2)
Simplifying:
Resultant force magnitude = √(6400 + 3600)
= √(10000)
= 100 N
Therefore, the magnitude of the resultant force is 100N.