An object of mass 4kg, slides down a rough plane inclined at 30degree to the horizontal. Find the magnitude of the frictional force of the object when its acceleration has magnitude 2m/s^2.
To find the magnitude of the frictional force on the object, we first need to calculate the component of the gravitational force parallel to the incline. This component will be responsible for causing the acceleration of the object down the plane.
The component of the gravitational force parallel to the incline can be calculated as follows:
F_parallel = m * g * sin(theta)
F_parallel = 4kg * 9.81m/s^2 * sin(30°)
F_parallel = 4kg * 9.81m/s^2 * 0.5
F_parallel = 19.62 N
Now, we know that the net force acting on the object down the incline is equal to the component of the gravitational force parallel to the incline minus the frictional force:
Net force = F_parallel - f
Given that the acceleration of the object down the plane is 2m/s^2, we can write the equation:
Net force = m * a
F_parallel - f = m * a
19.62 - f = 4kg * 2m/s^2
19.62 - f = 8 N
f = 19.62 - 8
f = 11.62 N
Therefore, the magnitude of the frictional force on the object is 11.62 N.