Draw a sketch on a cartesian plane
Draw a sketch diagram of the net x component and the net y component for both questions
1. Forces of 10N horizontally to the left And 13N in the opposite direction; 1N and 5N vertically upwards. The positive x direction is towards the right
x force = 13 - 10 = 3 Newtons right
y force = 1 +5 = 6 Newtons up
To draw a sketch on a Cartesian plane, we will plot the points based on the given information.
1. Forces of 10N horizontally to the left and 13N in the opposite direction; 1N and 5N vertically upwards:
Let's start by creating a Cartesian plane with the x-axis and y-axis labeled.
1. For the 10N force horizontally to the left, we will plot a point at (-10, 0) on the Cartesian plane.
2. For the 13N force in the opposite direction, we will plot a point at (13, 0) on the Cartesian plane.
3. For the 1N force vertically upwards, we will plot a point at (0, 1) on the Cartesian plane.
4. For the 5N force vertically upwards, we will plot a point at (0, 5) on the Cartesian plane.
Now let's connect the points to visualize the sketch diagram of the net x and net y components.
For the net x component, we will draw a line connecting the points (-10, 0) and (13, 0).
For the net y component, we will draw a line connecting the points (0, 1) and (0, 5).
The resulting sketch diagram should show a horizontal line between -10 and 13 on the x-axis representing the net x component of the forces, and a vertical line between 1 and 5 on the y-axis representing the net y component of the forces.
To draw a sketch on a Cartesian plane, you will need to create two perpendicular axes. The horizontal axis is called the x-axis, and the vertical axis is called the y-axis. The point where the two axes intersect is called the origin.
For the first question, let's start by drawing the x component. Since we have a force of 10N horizontally to the left and another force of 13N in the opposite direction, we can represent these forces as arrows on the x-axis.
Draw an arrow pointing towards the left with a length of 10 units to represent the force of 10N. Then, draw another arrow pointing towards the right with a length of 13 units to represent the force of 13N in the opposite direction. The lengths of the arrows represent the magnitudes of the forces.
For the y component, we have a force of 1N vertically upwards and another force of 5N vertically upwards as well. We can represent these forces as arrows on the y-axis.
Draw an arrow pointing upwards with a length of 1 unit to represent the force of 1N. Then, draw another arrow pointing upwards with a length of 5 units to represent the force of 5N. Again, the lengths of the arrows represent the magnitudes of the forces.
Now, we have the four arrows representing the given forces. The net x component can be obtained by adding the x components of the individual forces, and the net y component can be obtained by adding the y components of the individual forces. To visualize this, draw a line connecting the tail of the first arrow to the head of the last arrow in the x-axis direction. This represents the net x component. Similarly, draw a line connecting the tail of the first arrow to the head of the last arrow in the y-axis direction. This represents the net y component.
Remember that the positive x direction is towards the right, so the net x component will be the difference between the magnitudes of the two forces on the x-axis. For example, if the force of 13N is greater than the force of 10N, the net x component would be 13N - 10N = 3N to the right.
Similarly, the net y component will be the sum of the magnitudes of the forces on the y-axis. If there are multiple forces in the same direction, simply add their magnitudes. For example, if the force of 5N is in addition to the force of 1N, the net y component would be 5N + 1N = 6N upwards.
Repeat the above steps to draw the sketch diagram for the second question, considering the given forces and the positive x direction towards the right.