A woman of mass 50 kg is swimming with a velocity of 1.6m/s. If she stops stroking and glides to a stop in the water, what is the impulse of the force that stops her?
To calculate the impulse of the force that stops the woman, we need to understand the concept of impulse. Impulse is the change in momentum of an object and is defined as the product of the force applied to the object and the time interval over which the force is exerted. It can be calculated using the formula:
Impulse = Force * Time
In this case, the woman is swimming with a velocity of 1.6 m/s, and she stops stroking and glides to a stop. When she comes to a stop, her final velocity is 0 m/s.
To determine the impulse, we need to find the change in momentum. The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum is represented as:
Momentum = Mass * Velocity
Initially, the woman's momentum is given by:
Initial Momentum = Mass * Initial Velocity
Final momentum, when she comes to a stop, is given by:
Final Momentum = Mass * Final Velocity
Since the final velocity is 0 m/s, the final momentum will also be 0.
Now, let's calculate the impulse using the equation:
Impulse = Change in Momentum = Final Momentum - Initial Momentum
Since the final momentum is 0, the impulse is equal to the initial momentum (since change in momentum = 0).
Therefore, the impulse of the force that stops the woman is equal to her initial momentum.
Substituting the values, we have:
Impulse = Mass * Initial Velocity
Impulse = 50 kg * 1.6 m/s
Impulse = 80 N·s (Newton-seconds)
So, the impulse of the force that stops the woman is 80 Newton-seconds.