Kandi is dropping water balloons of different sizes from a rooftop to the ground. All of the water balloons experience the same rate of acceleration toward the ground and travel the same distance.
As she drops water balloons of increasing mass,
A. the force with which they strike the ground increases linearly.
B. the force with which they strike the ground increases exponentially.
C. the velocity at which they strike the ground increases exponentially.
energy at impact=mgh
1/2 mv^2=mgh
v=sqrt(2gh)
now assuming the time of contact with the ground is the same,
impactImpulse=change velocity
Force*timeImpact=change velocity
Force= sqrt(2gh)/timeImpact So None are correct with the identical time assumption. What about assuming the distance each moves into the earth is the same:
energyAsorbtion=final KE
F*distance=1/2 m v^2
Force= mgh/distance. So as mass increases, the force increases linearly with this assumption.
Thank you!
To answer this question, we need to analyze the effect of increasing mass on the force and velocity with which the water balloons strike the ground. Let's break down the options:
A. The force with which they strike the ground increases linearly.
To determine if the force increases linearly, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). Since we are told that all the water balloons experience the same rate of acceleration, we can assume that the acceleration will remain constant. If we increase the mass (m) while keeping the acceleration (a) constant, the force (F) will also increase linearly. Therefore, option A could be a valid answer.
B. The force with which they strike the ground increases exponentially.
If the force increased exponentially, it would mean that the force grows rapidly with increasing mass. However, according to Newton's second law, the force increases linearly with increasing mass when the acceleration is constant. Therefore, option B is incorrect.
C. The velocity at which they strike the ground increases exponentially.
While increasing the mass of the water balloons will affect the force, it will not directly affect the velocity at which they strike the ground. The acceleration due to gravity is constant, regardless of the mass of the object. Therefore, option C is also incorrect.
Based on the analysis, the correct answer is option A: the force with which the water balloons strike the ground increases linearly as their mass increases.