If a sphere and paper are dropped from 10 meters and the sphere hit the ground in 1.4 seconds and the paper hit in 2 seconds, why did the impact time in case of the piece of paper change in comparison to the sphere?
A. a=(Wt-R)/m;a=g B. a=(Wt-R)/m;a>g
C. a=(Wt-R);a<g D. a=(Wt-R)/m;a<g
To determine why the impact time of the piece of paper changed in comparison to the sphere, we need to analyze the forces acting on each object.
The sphere experiences two forces: its weight (W) acting downwards and the opposing force known as the normal force (R) provided by the ground. The net force acting on the sphere is the difference between the weight and the normal force, which can be written as Wt - R.
We can apply Newton's second law to the sphere: F = ma, where F is the net force and a is the acceleration. Since the acceleration due to gravity is directed downwards, we can express it as a = g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Let's examine the options provided:
A. a = (Wt - R)/m; a = g
This option suggests that the acceleration of the sphere is equal to the acceleration due to gravity, which is not correct because the net force acting on the sphere is not equal to its weight.
B. a = (Wt - R)/m; a > g
This option suggests that the acceleration of the sphere is greater than the acceleration due to gravity, which is also incorrect as the acceleration due to gravity remains constant regardless of the object.
C. a = (Wt - R); a < g
This option suggests that the acceleration of the sphere is less than the acceleration due to gravity, which is incorrect as the sphere is affected by gravity.
D. a = (Wt - R)/m; a < g
This option suggests that the acceleration of the sphere is less than the acceleration due to gravity, which is correct because the net force acting on the sphere is less than its weight.
Therefore, the appropriate answer is D. a = (Wt - R)/m; a < g.
Now, considering the piece of paper, it experiences air resistance in addition to the weight and normal force. The presence of air resistance affects the motion of the paper, causing it to take longer to reach the ground compared to the sphere. The impact time for the paper is increased due to the opposing force of air resistance.
Hence, the impact time of the paper changed in comparison to the sphere because the paper experiences air resistance, which slows down its descent.