To find the force exerted by one object on another, considering the applied force, masses of both objects, and friction forces, you can follow these steps:
Determine the net force acting on the first object: Start by calculating the net force acting on the first object. This force is the vector sum of the applied force and the frictional force acting on the object. If the applied force is greater than the frictional force, the net force will be the difference between the two. If the frictional force is greater, the net force will be zero since the object will not move.
Calculate the acceleration of the first object: Once you have the net force, you can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The equation is given by: F_net = m₁ * a, where F_net is the net force, m₁ is the mass of the first object, and a is its acceleration. Rearranging the equation, you get: a = F_net / m₁.
Determine the force exerted by the first object on the second object: Now that you have the acceleration of the first object, you can apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force exerted by the first object on the second object is equal in magnitude and opposite in direction to the force exerted by the second object on the first object. Therefore, the force exerted by the first object on the second object is F₁₂ = -m₂ * a, where m₂ is the mass of the second object.
Note: The negative sign in front of m₂ * a indicates that the force is in the opposite direction to the acceleration.
It's important to note that these calculations assume the objects are in direct contact and interact solely through the forces mentioned. If there are additional external forces or complexities involved, such as non-contact forces, you may need to consider them in your analysis.