Part A
In the photo at right, Sgt. 1st Class Cheryl Stearns of the U.S. Army's Golden Knights parachute team demonstrates how to maximize acceleration during a skydive (photo by Cpl. Sean Capogreco courtesy U.S. Army). Suppose that a 75 kg skydiver was using this technique. If the skydiver's current acceleration is 2.0 m/s 2 toward the ground, what is the force of air resistance acting on the skydiver?
System: The skydiver will be treated as a point particle subject to external influences from the earth (gravity) and the air.
Model: Point Particle Dynamics.
Approach: The free body diagram for this situation is:
FBD--GRAV BIGGER
When drawing a free body diagram for an object moving vertically under the influence of gravity and some other force(s), it is important to try to decide whether gravity is "winning" over the other force(s) or not. In this case, we know that the skydiver is accelerating toward the ground, so we expect that the force of gravity is larger than the force of air resistance. If you can come to such a conclusion, it is a good idea to represent it in your free body diagram.
The x-direction is unimportant in this problem, so we write only the y-component equation of Newton's Second Law:
\begin
[ \sum F_
= F_
- mg = ma_
] \end
This equation has only one unknown, so we can solve for Fair.
\begin
[ F_
= mg+ma_
= 735\:
+ (75\:
)(-2.0\:
^
) = 585\:
] \end
This problem illustrates the importance of choosing a coordinate system. Only by explicitly choosing the y-direction (as we did in the free body diagram) will you remind yourself that the acceleration is downward, and so an appropriate sign must be applied. In our case, because we chose the positive y-direction to be upward, the acceleration must be negative.
As we predicted in the note above, the force of air resistance is smaller than the force of gravity on the skydiver in this case.
Part B
In the photo at right, Sgt. 1st Class Cheryl Stearns of the U.S. Army's Golden Knights parachute team demonstrates how to maximize acceleration during a skydive (photo by Cpl. Sean Capogreco courtesy U.S. Army). Suppose that a 75 kg skydiver was using this technique. If the skydiver's current acceleration is 2.0 m/s 2 toward the ground, what is the force of air resistance acting on the skydiver?
System: The skydiver will be treated as a point particle subject to external influences from the earth (gravity) and the air.
Model: Point Particle Dynamics.
Approach: The free body diagram for this situation is:
FBD--GRAV BIGGER
When drawing a free body diagram for an object moving vertically under the influence of gravity and some other force(s), it is important to try to decide whether gravity is "winning" over the other force(s) or not. In this case, we know that the skydiver is accelerating toward the ground, so we expect that the force of gravity is larger than the force of air resistance. If you can come to such a conclusion, it is a good idea to represent it in your free body diagram.
The x-direction is unimportant in this problem, so we write only the y-component equation of Newton's Second Law:
\begin
[ \sum F_
= F_
- mg = ma_
] \end
This equation has only one unknown, so we can solve for Fair.
\begin
[ F_
= mg+ma_
= 735\:
+ (75\:
)(-2.0\:
^
) = 585\:
] \end
This problem illustrates the importance of choosing a coordinate system. Only by explicitly choosing the y-direction (as we did in the free body diagram) will you remind yourself that the acceleration is downward, and so an appropriate sign must be applied. In our case, because we chose the positive y-direction to be upward, the acceleration must be negative.
As we predicted in the note above, the force of air resistance is smaller than the force of gravity on the skydiver in this case.