Forces: Maintaining Equilibrium or Changing Motion

Learning Objectives:

• Better understand what a force is and how it affects on object; distinguish force from mass

• Classify and compare different forces, including: (1) internal and external, (2) contact and non-contact, and (3) friction and normal

• Determine the resultant of two or more forces using vector addition

• Resolve a resultant force into orthogonal components using vector resolution

• Discuss static equilibrium and its role in biomechanics

Introduction to Forces

Force:

1. is a push or a pull

2. has the ability to accelerate an object (ΣF = ma)

3. is usually measured in units of Newtons (N) or pounds (lb).

1N = 0.225lb and 1lb = 4.45N; Now, using this conversion, calculate your body weight in N. Also, Using Newton's 2nd Law (ΣF = ma), and the acceleration due to gravity, calculate your mass in kg.

Classification of Forces

1. Internal forces: forces that act within the object or system whose motion is being investigated. Alone, these forces cannot change the motion of the body center of mass.

2. External forces: forces that act on an object as a result of its interaction with the environment surrounding it. These forces can change the motion of the body center of mass. Many sport biomechanists are concerned most with external forces.

a. Contact forces: most of the forces we will discuss this semester are contact forces (these can include internal and external) that occur from contacting objects including solids and fluids. It is often helpful to resolve these forces into two categories that are based upon direction: friction (F_F) and the normal (F_N) force.

F_F = F_N × μ

Friction force: the component of the contact force that acts parallel to the contact surfaces. There is static and dynamic friction. Static friction > dynamic friction.

Friction opposes motion, yet is also responsible for horizontal motion. With the aforementioned equation in mind, how can you increase friction for any given circumstance?

A somewhat related, interesting discussion on race car tires...

Normal Contact Force: the component of a contact force that acts perpendicular to the contact surfaces; normal and friction forces are both essential to human movement.

Practice Problem: If a runner exerts a vertical force of 2000 N, and the coefficient of static friction between the shoe and the ground is 0.50, what is the maximum horizontal force he can generate under his shoe before sliding? Answer 1000 N. What can the runner change to enable him to apply more horizontal force without slipping?

Practice Problem: You are trying to pull someone on a sled, via a rope that is attached to the sled, across a flat snowy field. Your pulling force is directed forward and upward, at an angle that is 30 degrees above the ground. The combined mass of the person on the sled and the sled is 58 kg, and the coefficient of static friction between the sled and the snow is 0.10. How much force must you pull with to start moving the sled? Answer: ~62N

b. Non-contact forces: forces that do not require contact between two objects. The non-contact force of primary concern is gravity, which causes an acceleration of -9.81 m/s/s, no matter how large or small the object is.

The Analysis of Multiple, Simultaneous Forces

What happens when there is more than one force?

A free body diagram is a tool for analyzing forces. It is a drawing of the object under consideration that includes external forces that are acting upon the object. These forces are vector quantities that are represented using arrows. The arrows represent the force points of application, force direction, and force magnitude.

To simultaneously consider multiple colinear forces (two or more forces that have the same line of action, but not necessarily the same direction), only simple algebra is needed.

To simultaneously multiple non-colinear forces, you cannot algebraically sum each of the forces. You must use vector addition: the addition of two or more non-colinear vectors, resulting in a resultant force.

Practice Problem: The peak normal contact force for a runner is 1800 N and the simultaneous frictional force is 200 N. What does the magnitude of the resultant ground reaction force equal? Answer: 1811 N. Also, at what angle, in relation to the horizontal axis, is this resultant ground reaction force applied? Answer: 84 degrees above the horizontal axis

Another practice problem: Using vector addition, calculate the resultant force acting on this gymnast. Answer: 51 N.

Vector resolution is also an important skill to have for biomechanical analyses. Vector resolution allows you to resolve one resultant force into perpendicular components. This might be thought of as the opposite of vector composition.

Practice Problem: What are the magnitudes of the vertical and horizontal components of a resultant ground reaction force (4500 N) that is applied to a long jumper at an orientation that is 20 degrees above the ground? Answer: Vertical component = 1539 N; Horizontal Component = 4229 N.

Static Equilibrium (ΣF = 0)

Additional Practice Problems:

1. Calculate the reaction forces applied to the child on a swing, assuming that the child is in static equilibrium (ΣF = 0). Calculate the resultant reaction force (F_R), the two separate components of the resultant reaction force (F_RX & F_RY), and the orientation of the reaction force in relation to the horizontal (θ). Answer: 194 N, oriented 78 degrees above the horizontal axis.

2. The quadriceps pulls on the patella with a force of 1000 N. The patellar tendon also pulls on the patella with a force of 1000 N. A force from the femoral condyles is the only other significant force acting on the patella. If the patella is in static equilibrium and the knee is flexed to 120 degrees, what must the magnitude of the force that is applied to the patella by the femur be? Answer: 1000 N.

Chapter One Summary

1. Forces are pushes or pulls that can be represented by vector quantities.

2. External forces can cause changes in the motion of the center of mass; the most common are gravity and contact forces.

3. Friction and normal forces constitute contact forces.

4. Vector composition and resolution are important tools in the analysis of forces.

5. Static equilibrium indicates that the sum of all external forces equals zero (ΣF_x = 0 and F_y = 0).