A 175-N box is placed on an inclined plane that makes a 20.0° angle with the horizontal. Find the component of the weight force parallel to the plane's surface.
175 sin 20
The way to remember this is to think of the box on a level floor.
Then the component parallel to the surface is obviously zero.
and sure enough sin 0 = 0
the normal component is the entire weight when the surface is level
and sure enough cos 0 = 1
To find the component of the weight force parallel to the plane's surface, we need to calculate the weight force first.
The weight force (Fg) can be calculated using the formula:
Fg = m * g
Where "m" is the mass of the box and "g" is the acceleration due to gravity.
We are given the weight of the box, which is 175 N. Since weight = mass * gravity, we can rearrange the equation to solve for mass:
m = Fg / g
Assuming the acceleration due to gravity is 9.8 m/s^2, we can substitute the given values into the equation:
m = 175 N / 9.8 m/s^2
m ≈ 17.9 kg
Now, we can find the component of the weight force parallel to the plane's surface.
The component of the weight force parallel to the plane's surface (F_parallel) can be calculated using the formula:
F_parallel = Fg * sin(theta)
Where "theta" is the angle between the plane and the horizontal.
Substituting the values into the equation:
F_parallel = 175 N * sin(20.0°)
F_parallel ≈ 59.6 N
Therefore, the component of the weight force parallel to the plane's surface is approximately 59.6 N.
To find the component of the weight force parallel to the plane's surface, we need to use some trigonometry. Let's break it down step by step:
Step 1: Identify the given information:
- Weight force: 175 N
- Angle of the inclined plane with the horizontal: 20.0°
Step 2: Draw a diagram:
Draw a diagram of the inclined plane and label the given angle (20.0°) and the weight force (175 N) acting vertically downward.
Step 3: Determine the components of the weight force:
Since the weight force acts vertically downward, it can be divided into two components: one parallel to the inclined plane and the other perpendicular to the inclined plane.
Step 4: Calculate the component parallel to the inclined plane:
The weight force can be divided into two components: one perpendicular to the inclined plane (normal force) and one parallel to the inclined plane (component we are trying to find).
To find the component of the weight force parallel to the inclined plane (F_parallel), we use the formula:
F_parallel = F * sinθ
Where:
F is the weight force (175 N)
θ is the angle of the inclined plane (20.0°)
Step 5: Solve for the component parallel to the inclined plane:
F_parallel = 175 N * sin(20.0°)
Step 6: Calculate the answer:
Using a calculator, find the sine of 20.0° and multiply it by 175 N:
F_parallel ≈ 59.74 N
Therefore, the component of the weight force parallel to the inclined plane is approximately 59.74 N.