a 2kg on a smooth inclined plane is connected over a smooth pulley to a mass as shown above the acceleration of the system is,?
To find the acceleration of the system, we need to consider the forces acting on the objects involved.
In this case, we have a 2kg mass on a smooth inclined plane connected to another mass over a smooth pulley. Let's assume the other mass is M kg.
First, let's consider the 2kg mass on the inclined plane. The only force acting on it is gravity, which can be split into two components: the force pulling it down the inclined plane (mg*sinθ) and the force perpendicular to the plane (mg*cosθ).
Next, let's consider the mass connected over the smooth pulley. Since it is connected by a rope passing over a smooth pulley, the tension in the rope will be the same on either side of the pulley. Therefore, the tension in the rope will be equal to the gravitational force acting on the 2kg mass (Tension = mg*sinθ).
Now, let's analyze the net force acting on the 2kg mass. The net force is given by the difference between the force pulling it down the inclined plane (mg*sinθ) and the force perpendicular to the plane (mg*cosθ). So, the net force (Fnet) is:
Fnet = mg*sinθ - mg*cosθ
Since the acceleration (a) of an object is related to the net force acting on it (Fnet) by Newton's second law (Fnet = ma), we can rearrange the equation to find the acceleration:
a = Fnet / m
Substituting the expression for Fnet we found earlier, we get:
a = (mg*sinθ - mg*cosθ) / m
Simplifying further, we get:
a = g*(sinθ - cosθ)
Thus, the acceleration of the system is g times the difference between the sine and cosine of the angle of inclination (θ) of the plane.