A body of mass 2kg is placed on a rough inclined plane ,whose angle of inclination is 30°.
Find the force acting down the slope and the acceleration if a frictional force of 5N acts between the body and the surface?
down the slope due to gravity=mg*sinTheta
up the slope due to friction: 5N
net force down slope= forceduegravity-friction=ma
a= g*sinTheta-5/m
To find the force acting down the slope and the acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the force component acting down the slope. We can break the weight of the object into two components: one along the slope and the other perpendicular to the slope. The force component acting down the slope is given by the equation:
Force down the slope = weight of the object * sin(angle of inclination)
The weight of the object can be calculated using the equation:
Weight = mass of the object * gravitational acceleration
In this case, the mass of the object is 2 kg and the gravitational acceleration is approximately 9.8 m/s^2. Therefore,
Weight = 2 kg * 9.8 m/s^2 = 19.6 N
Now, we can calculate the force component acting down the slope:
Force down the slope = 19.6 N * sin(30°) ≈ 9.8 N
Next, let's calculate the net force acting down the slope. The net force is given by the equation:
Net force = Force down the slope - Frictional force
In this case, the frictional force is given as 5 N. Therefore,
Net force = 9.8 N - 5 N = 4.8 N
Finally, we can use Newton's second law to find the acceleration:
Acceleration = Net force / mass of the object
Acceleration = 4.8 N / 2 kg = 2.4 m/s^2
Therefore, the force acting down the slope is 9.8 N and the acceleration is 2.4 m/s^2.