Understanding the Forces
* Gravity (mg): The force acting vertically downwards due to the Earth's gravity (m = mass, g = acceleration due to gravity ≈ 9.8 m/s²).
* Normal Force (N): The force exerted by the inclined plane perpendicular to its surface.
* Force of Friction (f): The force opposing the motion of the body along the inclined plane.
The Key Equation
The acceleration of the body down the inclined plane is determined by the net force acting on it, which is the component of gravity acting parallel to the plane minus the force of friction:
* a = (mg sinθ) - f
* θ is the angle of the incline.
Analyzing the Condition
We are given that the acceleration (a) is 4.9 m/s². To find the condition, we need to understand the relationship between the angle of the incline (θ) and the force of friction (f).
* Frictionless Surface: If the surface is frictionless (f = 0), then the equation simplifies to:
* a = g sinθ
* To get an acceleration of 4.9 m/s², we need:
* sinθ = 4.9 / 9.8 = 0.5
* θ = 30°
* Surface with Friction: If there is friction, we need more information about the coefficient of friction (μ) between the body and the inclined plane. The force of friction is given by:
* f = μN
* N = mg cosθ (component of gravity perpendicular to the plane)
In Conclusion
The condition for a body on an inclined plane to have an acceleration of 4.9 m/s² depends on the presence and magnitude of friction:
* Without friction: The angle of inclination must be 30°.
* With friction: The angle of inclination and the coefficient of friction will need to be calculated to satisfy the equation:
* a = (g sinθ) - μ(mg cosθ) = 4.9 m/s²
Let me know if you have specific information about the coefficient of friction, and I can help you calculate the angle of inclination for that situation.
