How to calculate a gravitational force exerted on the paralle to the incline if its mass is 20kg is pulled upwards by a force inclined at 30 degree to the horizontal nd it accelerate along the incline plane at 2m.s-2?
Neglecting friction?
What force?
To calculate the gravitational force exerted on the parallel to the incline, we need to break down the forces acting on the object.
1. Identify the forces:
- Gravitational force (Fg): This is the force exerted on the object due to gravity. It acts vertically downward and can be calculated using the formula: Fg = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s²).
- Force inclined at 30 degrees (Fi): This is the force pulling the object upwards along the incline. It is inclined at an angle of 30 degrees to the horizontal.
- Normal force (Fn): This is the force exerted by the surface of the incline on the object perpendicular to the incline. It is equal in magnitude but opposite in direction to the component of the gravitational force acting along the incline.
2. Resolve the forces:
- Resolve the gravitational force into two components: one perpendicular to the incline (Fn), and one parallel to the incline (Fg-parallel).
- Fn = Fg * cos(θ), where θ is the angle of the incline with respect to the horizontal.
- Fg-parallel = Fg * sin(θ).
3. Calculate the gravitational force parallel to the incline (Fg-parallel):
- First, calculate the gravitational force (Fg) using the formula: Fg = m * g.
- Substitute the value of Fg into the equation for Fg-parallel: Fg-parallel = Fg * sin(θ).
- Remember to convert the angle from degrees to radians when using trigonometric functions. (sin(30°) ≈ 0.5)
4. Determine the gravitational force parallel to the incline by applying Newton's second law:
- Apply Newton's second law (F = m * a) to the object's motion along the incline.
- The gravitational force parallel to the incline (Fg-parallel) is equal to the mass of the object (m) multiplied by the acceleration along the incline (a).
- Rearrange the formula to find Fg-parallel: Fg-parallel = m * a.
By following these steps, you can calculate the gravitational force exerted on the object parallel to the incline.