Calculate the components parallel and perpendicular to the plane of 150N gravitational force acting on an object on a slope at 20 degrees to the horizontal ?
M*g = 150 N.
Fp = 150*sin20 = Force parallel.
Fn=150*Cos20 = Normal or perpendicular.
To calculate the components parallel and perpendicular to the plane of the gravitational force acting on an object on a slope, we need to consider the angle at which the slope is inclined. In this case, the slope is inclined at 20 degrees to the horizontal.
Step 1: Draw a free-body diagram of the object on the slope, indicating the gravitational force (150N) acting vertically downwards.
Step 2: Resolve the gravitational force into component vectors. The component parallel to the slope is the force that tends to move the object down the slope, and the component perpendicular to the slope acts perpendicular to the slope.
Step 3: Calculate the parallel component (F_parallel):
F_parallel = F_gravity * sin(angle)
F_parallel = 150N * sin(20°)
F_parallel ≈ 50.94N
Step 4: Calculate the perpendicular component (F_perpendicular):
F_perpendicular = F_gravity * cos(angle)
F_perpendicular = 150N * cos(20°)
F_perpendicular ≈ 142.80N
So, the components parallel and perpendicular to the plane of the gravitational force acting on the object on the slope at 20 degrees to the horizontal are approximately:
Parallel component: 50.94N
Perpendicular component: 142.80N
To calculate the components parallel and perpendicular to the plane of the gravitational force acting on an object on a slope, we need to consider the force's vector components.
1. Break down the gravitational force into its components:
- The component parallel to the slope is the force that acts down the slope.
- The component perpendicular to the slope is the force that acts perpendicular to the slope.
2. Determine the angle between the gravitational force vector and the slope:
- In this case, the slope angle is given as 20 degrees to the horizontal.
3. Calculate the components:
- The parallel component can be found by multiplying the gravitational force by the cosine of the angle between the force vector and the slope.
Parallel component = Gravitational force * cos(angle)
- The perpendicular component can be found by multiplying the gravitational force by the sine of the angle between the force vector and the slope.
Perpendicular component = Gravitational force * sin(angle)
4. Substitute the given values into the equations:
Given:
Gravitational force = 150N
Angle = 20 degrees
Parallel component = 150N * cos(20 degrees)
Perpendicular component = 150N * sin(20 degrees)
5. Calculate the results using a calculator:
Parallel component = 150N * cos(20 degrees) ≈ 140.51 N
Perpendicular component = 150N * sin(20 degrees) ≈ 51.39 N
Therefore, the components of the gravitational force acting on the object on the slope are approximately 140.51 N parallel to the slope and 51.39 N perpendicular to the slope.