Forces: Maintaining Equilibrium or Changing Motion

Objectives:

• Define force
• Classify forces: Internal vs External, Contact vs Non-contact, and Friction vs Normal
• Distinguish the difference between mass and weight
• Determine the resultant of two or more forces (vector addition)
• Resolve a resultant force into component forces acting at right angles to each other (vector resolution)
• Determine whether an object is in static equilibrium, if the forces acting on the object are known
• Detemine an unknown force acting on an object, if all the other forces acting on the object are known and the object is in static equilbrium

Introduction to Forces

A force is a push or a pull.
A force is something that has the ability to accelerate an object.

Forces are described in units of Newtons (N) or pounds (lb)

1 N will accelerate 1 kg at 1 m/s/s (F=ma)

Also, 1N = 0.225lb and 1lb = 4.45N
 

Using Newton's 2nd Law (F=ma), how much do you weigh?

Classification of Forces

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.

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 only concerned with external forces.

Contact forces: forces that exert force as a result of two objects contacting one another. These objects can be solid or fluid.

 

Non-contact forces:

Gravity: causes an acceleration of -9.81 m/s/s, no matter how large or small the object is; so, how many N does one kg of mass weigh? (remember F = m · a)

External forces may be further divided into two groups; these two groups are based upon direction:

1. Friction force: the component contact force that acts parallel to the surfaces in contact (due to the interactions of surface molecules). There is static and dynamic friction, and static friction > dynamic friction. The mathematical description of friction is: Friction Force = μ × Normal Force. Friction opposes motion, yet is also responsible for all horizontal motion.

2. Normal Contact Force: the component of a contact force that acts perpendicular to the surfaces in contact; both the normal and friction forces are 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?

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 analysis object with all external forces acting upon the object represented as arrows showing their points of application and directions.

Colinear forces: two or more forces that have the same line of action, but not necessarily the same direction; when adding these types of forces, one can use simple algebra.

Colinear Forces Practice Problem

Concurrent forces: two or more forces whose lines of action intersect at a single point. If these force are not colinear, you cannot algebraically sum each of the forces. You must use vector addition.

Vector addition, or composition: the addition of two or more non-colinear vectors, resulting in a resultant force.

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

Vector resolution allows you to resolve one resultant force into perpendicular components; this might be thought of as the opposite of vector composition.

Vector Resolution Practice Problem: What are the magnitudes of the vertical and horizontal components of a resultant ground reaction force with a magnitude of 1500 N and orientation that is 75 degrees above horizontal?

Quiz Question, January 22

During one step in the middle of a race, a sprinter pushes against the ground with a resultant force of 2350 N, at an angle of 80° relative to the ground. What is the horizontal component of this force?

a. 414 N

b. 2314 N

c. 2350 N

d. None of the above



Static Equilibrium (ΣF = 0)

When an object is at rest and the forces acting on the object are in equilibrium, they result in a net force of zero. Weightlifter example: The acceleration of this weightlifter is zero. If this person's mass = 80kg, and the mass of the barbell = 70kg, what must the ground reaction force equal? Fgrf + Fbw + Fbb = 0 What would occur if the ground reaction force applied to the weightlifter = 2000 N? How might this occur?

Additional Practice Problems:

1. Using vector addition, calculate the resultant force acting on this gymnast
2. 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).
3. 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?

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).