a body of mass 20kg slides down on a plane inclined of 30 degree to the horizontal. if a constant resisting force of 40N act on the body, it's a acceleration down the plane is?
To find the acceleration of the body down the inclined plane, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = m * a).
In this case, we have a few forces acting on the body:
1. The component of the gravitational force that acts parallel to the inclined plane (mg * sinθ), where m is the mass of the body (20 kg) and θ is the angle of inclination (30 degrees).
2. The resisting force (40 N) that acts in the opposite direction to the motion.
The net force is the difference between these two forces:
Net force = mg * sinθ - resisting force
Substituting the given values:
Net force = (20 kg) * (9.8 m/s^2) * sin(30 degrees) - 40 N
Now, we can rearrange Newton's second law to solve for acceleration:
a = Net force / m
a = [(20 kg) * (9.8 m/s^2) * sin(30 degrees) - 40 N] / 20 kg
Evaluating the expression, we can find the acceleration.
Note: Make sure to convert the angle from degrees to radians when using trigonometric functions. In this case, sinθ = sin(30 degrees) = sin(π/6) = 0.5.