A body of mass 4 kg resting on a smooth horizontal plane is simultaneously acted upon by two perpendicular forces 6N and 8N. Calculate the acceleration of t...

Answer Details

To find the acceleration of the motion, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this problem, the body has a mass of 4 kg and is acted upon by two perpendicular forces of 6N and 8N. Since the plane is smooth, there is no frictional force acting on the body. Therefore, the net force acting on the body is the vector sum of the two perpendicular forces. Using the Pythagorean theorem, we can find the magnitude of the net force: Net force = sqrt((6N)^2 + (8N)^2) = 10N The direction of the net force is the angle formed between the two perpendicular forces: tan θ = (8N)/(6N) => θ = tan^-1(8/6) = 53.13° The net force is at an angle of 53.13° to the horizontal. Now, we can calculate the acceleration using Newton's second law: acceleration = net force / mass acceleration = 10N / 4kg acceleration = 2.5 ms^-1 Therefore, the acceleration of the motion is 2.5 ms^-1.