Final answer:
Momentum is the product of mass and velocity, while impulse is equal to the force applied to an object multiplied by the time it is applied. An object's change in momentum is equal to the impulse delivered by the force. In cases where the same mass is subject to different forces over different times, the change in momentum depends on the product of force and time.
Step-by-step explanation:
The momentum of an object is the product of its mass and velocity, which is typically represented by the equation p = m × v. The change in momentum (Δp) referred to as impulse, is equal to the product of the force (F) applied to an object and the time (t) for which it is applied, expressed as J = F × t. When a force is applied over time, it changes the object's momentum, and the impulse delivered by the force is equal to this change in momentum.
For example, if a force of 50 N is applied to an object for 0.2 s, and the object's velocity changes by 10 m/s, we use the formula F × t = m × (Δv) to find the mass. We rearrange it to m = (F × t) / (Δv). Plugging in the values gives us m = (50 N × 0.2 s) / (10 m/s), which calculates to a mass of 1 kg.
In scenarios involving two objects with the same mass where different forces act for different amounts of time, the change in momentum or impulse for each object will depend on the product of the force and the time. If 100 N acts on the first object for 1 s and on the second object for 2 s, assuming no other forces are at play, the second object will experience a greater impulse because impulse is directly proportional to time. Hence, the second object will undergo a greater change in momentum.