a lawn mower is pushed up a 15degree slope by a 20lb force. Find the component acting parallel to the slope
To find the component of the force acting parallel to the slope, we need to find the vector components of the force.
Given:
Force (F) = 20 lb
Angle of the slope (θ) = 15 degrees
To find the component of the force acting parallel to the slope, we can use trigonometry. The component we need is the one that lies along the slope, which is the force's horizontal component.
Step 1: Convert the angle from degrees to radians.
θ (in radians) = (15 degrees) × (π/180 degrees)
θ (in radians) = 0.2618 radians
Step 2: Find the horizontal component of the force.
The horizontal component (F_x) can be calculated using the formula:
F_x = F × cos(θ)
Substituting the values:
F_x = 20 lb × cos(0.2618 radians)
Step 3: Calculate the horizontal component.
Using a calculator, find the value of cos(0.2618 radians), which is approximately 0.9659.
F_x = 20 lb × 0.9659
F_x ≈ 19.318 lb
Therefore, the component of the force acting parallel to the slope is approximately 19.318 lb.
To find the component of the force acting parallel to the slope, we need to calculate the vertical force and then find its component along the slope.
Given:
- Force applied: 20 lb
- Angle of the slope: 15 degrees
Step 1: Find the vertical force (perpendicular to the slope)
The vertical force is given by the equation:
Vertical Force = Applied Force * sin(Angle)
Vertical Force = 20 lb * sin(15 degrees)
Using this equation, we can calculate the vertical force:
Vertical Force = 20 lb * 0.258819
Vertical Force ≈ 5.176 lb
Step 2: Find the component of the vertical force acting along the slope
The component of the force acting parallel to the slope is given by the equation:
Component along slope = Vertical Force * cos(Angle)
Component along slope = 5.176 lb * cos(15 degrees)
Using this equation, we can calculate the component along the slope:
Component along slope = 5.176 lb * 0.965926
Component along slope ≈ 4.999 lb (rounded to three decimal places)
Therefore, the component of the force acting parallel to the slope is approximately 4.999 lb.