A create is pulled across a horizontal surface with a force of 100N which makes an angle of 30 degrees with a horizontal.(a)draw a diagram of the horizontal and vertical components of the force.(b)resolve the force in its parallel and perpendicularcomponents of the force.
(a) To draw a diagram of the horizontal and vertical components of the force, we can use trigonometry.
The given force is 100N and it makes an angle of 30 degrees with the horizontal. We can start by drawing a coordinate system with a horizontal axis (x-axis) and a vertical axis (y-axis). Then, draw a line representing the given force at an angle of 30 degrees to the horizontal.
Next, we can draw a dotted line perpendicular to the x-axis from the tip of the force vector. This represents the vertical component of the force.
Finally, we can draw a dotted line parallel to the x-axis from the tip of the force vector. This represents the horizontal component of the force.
The resulting diagram should look like this:
```
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____|___(100N)
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|/
```
(b) To resolve the force into its parallel and perpendicular components, we can use trigonometry.
The vertical component of the force can be found by using the formula:
Vertical component = Force × sin(angle)
Vertical component = 100N × sin(30 degrees)
Vertical component = 100N × 0.5
Vertical component = 50N
The horizontal component of the force can be found by using the formula:
Horizontal component = Force × cos(angle)
Horizontal component = 100N × cos(30 degrees)
Horizontal component = 100N × 0.866
Horizontal component ≈ 86.6N
So, the resolved force components are approximately:
- Vertical component: 50N
- Horizontal component: 86.6N
To answer the question, let's break it down into two parts:
(a) Drawing a diagram of the horizontal and vertical components of the force:
To visualize the horizontal and vertical components of the force, draw a horizontal line to represent the surface and then draw a line at a 30-degree angle above the horizontal line to represent the force of 100N.
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F / |
o / |
r / |
c 30°|
e /|
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/
The horizontal component (Fx) of the force can be represented by the length of the line projected onto the horizontal axis, while the vertical component (Fy) can be represented by the length of the line projected onto the vertical axis.
(b) Resolving the force into its parallel and perpendicular components:
To calculate the parallel and perpendicular components of the force, we need to use trigonometry.
The parallel component of the force (Fp) is given by: Fp = F * cos(theta)
The perpendicular component of the force (Fn) is given by: Fn = F * sin(theta)
Here, F represents the magnitude of the force (100N) and theta represents the angle with the horizontal (30 degrees).
To calculate Fp and Fn, plug in the values:
Fp = 100N * cos(30°)
Fn = 100N * sin(30°)
Calculating these values will give you the resolved components of the force.