How is it possible for an object to obtain a larger impulse from a smaller force than from a larger force?
i have no clue how this can happen .....it seems impossible ..
what if the smaller force acts for a longer time?
impulse= force*actingtime
I can understand why this might seem counterintuitive, but actually, it is possible for an object to obtain a larger impulse from a smaller force compared to a larger force. To understand how this is possible, we need to first define impulse and understand the relationship between force, time, and impulse.
Impulse is defined as the product of the force applied to an object and the time interval over which the force acts. Mathematically, impulse (J) can be expressed as the integral of force (F) with respect to time (t) over a given time interval:
J = ∫ F dt
Now, consider two scenarios:
Scenario 1: Larger Force, Shorter Time
If a larger force is applied to an object over a relatively shorter time, the impulse will be greater compared to a smaller force applied over a longer time. This is because the area under the force-time graph (which represents impulse) will be larger when the force is larger, and the time interval is shorter.
Scenario 2: Smaller Force, Longer Time
Now, suppose a smaller force is applied to an object over a longer time interval. Although the force applied is smaller, the duration it acts is significantly longer. As a result, the area under the force-time graph can end up being greater than that of a larger force exerted over a shorter time interval.
To visualize this concept, imagine two people trying to stop a moving car. Person A pushes against the car with a huge amount of force for 1 second, while person B pushes against the car with a smaller force for 10 seconds. Even though person B exerts a smaller force, the total impulse they deliver to the car will be greater due to the longer time interval over which they apply the force.
So, in summary, an object can obtain a larger impulse from a smaller force compared to a larger force by exerting the smaller force over a longer period of time.