Using a scale of 1 cm to represent 10 N,find the size and direction of the resultant force for 30 N north and 40 N west .(make sure you have a grid paper and a protractor to do this question)
To find the size and direction of the resultant force, we can use vector addition. We'll first represent the given forces on a grid paper using the given scale and then find the result.
1. Start by drawing a horizontal line on the grid paper to represent the x-axis and a vertical line to represent the y-axis.
2. Choose a reference point as the origin (0,0) on the grid paper.
3. Since the scale is 1 cm = 10 N, for the 30 N force pointing north, draw an arrow upwards from the origin that is 3 cm long (30 N / 10 N/cm = 3 cm). Label it as F1.
4. For the 40 N force pointing west, draw an arrow to the left from the origin that is 4 cm long (40 N / 10 N/cm = 4 cm). Label it as F2.
5. Now, draw a vector from the origin that connects the tip of F1 to the tip of F2. This vector represents the resultant force F.
6. Measure the length of the resultant force vector on the grid paper. Let's say it measures 5.5 cm.
7. Convert the length back to Newtons using the scale of 1 cm = 10 N. So, 5.5 cm * 10 N/cm = 55 N.
8. The magnitude of the resultant force is 55 N.
9. To find the direction of the resultant force, use a protractor. Place the protractor on the grid paper with the reference line aligned along the positive x-axis (east). Measure the angle between the positive x-axis and the resultant force vector. Let's say it measures 35 degrees counterclockwise (west) from the positive x-axis.
10. The direction of the resultant force is 35 degrees counterclockwise from the positive x-axis or 35 degrees west of north.
So, the size of the resultant force is 55 Newtons and the direction is 35 degrees west of north.
To find the size and direction of the resultant force, we need to use vector addition. Here is how you can solve the problem:
1. Draw a coordinate grid on your grid paper with a horizontal x-axis and vertical y-axis. Make sure to label the axes.
2. Locate the starting point of the first force, which is 0 N north and 0 N west.
3. Draw an arrow from the starting point in the direction of the first force, which is 30 N north. Measure 3 cm (since 1 cm represents 10 N) and mark the endpoint of the arrow.
4. Now, locate the endpoint of the first force as the starting point for the next force. Draw an arrow from this starting point in the direction of the second force, which is 40 N west. Measure 4 cm (since 1 cm represents 10 N) and mark the endpoint of the arrow.
5. To find the resultant force, draw a straight line from the starting point of the first force to the endpoint of the second force. This line represents the resultant force.
6. Measure the length of the line in centimeters. Since 1 cm represents 10 N, you need to multiply the measured length by 10 to find the size of the resultant force.
7. To determine the direction of the resultant force, use a protractor to measure the angle between the x-axis and the line representing the resultant force.
8. If the angle is measured clockwise from the x-axis, then the direction is west of north. If the angle is measured counter-clockwise from the x-axis, then the direction is north of west. Note the angle and direction.
By following these steps, you can determine the size and direction of the resultant force using the given scale and the forces applied in the north and west directions.
Is that true that you have already solve this
Fr = -40 + 30i = 50 N. [-37o] = 50N.[37o] N. of W. = 50N.[143o] CCW.
I had to solve it by using vectors.