Acceleration and Increased Mass: A Fun Physics Problem to Solve!

How does the acceleration of an object change when its mass is increased by a factor of 4 while the same force is exerted on it?

Answer:

When the mass of an object is increased by a factor of 4 while the same force is exerted on it, the new acceleration will be one-fourth of the original acceleration.

When we talk about the acceleration of an object, it is essential to consider the relationship between force, mass, and acceleration as described by Newton's second law of motion. According to this law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Mathematically, we can express this relationship using the formula a = F/m, where 'a' represents acceleration, 'F' is the force applied, and 'm' is the mass of the object. In the given scenario, a workman exerts a force of 628 N while dragging a crate.

Initially, the acceleration of the crate can be represented as a = 628/m, where 'm' is the mass of the crate. When the mass of the crate is increased by a factor of 4, the new mass becomes 4m. Since the workman still exerts the same force of 628 N, the new acceleration can be calculated as a' = 628/(4m).

By comparing the old acceleration (a) with the new acceleration (a'), we can determine that the ratio a/a' is equal to 4. This indicates that the new acceleration is one-fourth of the original acceleration, showcasing the inverse relationship between mass and acceleration when the force remains constant.