Question

A block of mass 23 kg rests on a plane making an angle of 100 with horizontal. Determine the component of the weight normal to the plane. Select one: 1. 93.18 N 2. 22.22 N 3.39.18N 4. 222.20N​

Answer 1

Explanation:

To determine the component of the weight (mg) that acts normal (perpendicular) to the plane, you can use trigonometry. The component of the weight normal to the plane is given by:

F_normal = mg * cos(θ)

Where:

- F_normal is the component of weight normal to the plane.

- m is the mass (23 kg).

- g is the acceleration due to gravity (approximately 9.81 m/s²).

- θ is the angle between the weight and the normal direction (100 degrees).

Let's calculate it:

F_normal = 23 kg * 9.81 m/s² * cos(100°)

F_normal ≈ 23 kg * 9.81 m/s² * (-0.1736) (cos(100°) is approximately -0.1736)

F_normal ≈ -38.19 N

The component of the weight normal to the plane is approximately 38.19 N. However, since it's acting in the opposite direction of the gravitational force (upward), you should take its absolute value:

|F_normal| ≈ 38.19 N

So, the correct option is 3. 39.18 N.