What's the solution of a body of weight 100N resting on a plane which is inclined at 30° to the horizontal with the components of the weight parallel and perpendicular to the plane?

To find the components of the weight of the body parallel and perpendicular to the inclined plane, we will use trigonometry.

Step 1: Draw a diagram of the situation. Label the weight of the body as 100N and the angle of inclination as 30°.

Step 2: Decompose the weight vector into its components. The weight vector can be resolved into two components: one parallel to the inclined plane and one perpendicular to it.

Step 3: Find the perpendicular component of the weight. This can be found using trigonometry. In this case, the perpendicular component of the weight is equal to the weight multiplied by the sine of the angle of inclination.

Perpendicular Component = Weight * sin(Angle of Inclination)

Substituting the given values:

Perpendicular Component = 100N * sin(30°)

Step 4: Calculate the parallel component of the weight. This can be found using trigonometry as well. In this case, the parallel component of the weight is equal to the weight multiplied by the cosine of the angle of inclination.

Parallel Component = Weight * cos(Angle of Inclination)

Substituting the given values:

Parallel Component = 100N * cos(30°)

Step 5: Calculate the values using a calculator.

Perpendicular Component = 100N * 0.5 = 50N
Parallel Component = 100N * 0.866 = 86.6N (rounded to one decimal place)

Therefore, the perpendicular component of the weight is 50N, and the parallel component of the weight is approximately 86.6N.