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LESSON 2: FORCE AND MOTION
Introduction We commonly described the motion of particles based on the definition of displacement, velocity and acceleration. This lesson will describe the motion of bodies using the concepts of force and mass. Learning Outcomes After successful completion of this lesson, you should be able to: To learn Newton’s laws of motion To study the relationship between a force and the acceleration it causes To solve problems related to the Newton’s second law of motion To define frictional force and solve problems related to it Discussion 2.1 The Concept of Force When you push or pull an object, you exert a force on it. If an object moves with uniform motion ( constant velocity ), no force is required to maintain the motion. Only a force can cause a change in velocity that causes a body to accelerate. A Force is an interaction that causes an acceleration of a body. The magnitudes of forces are defined in terms of the acceleration they give the standard kilogram. A force that accelerates that standard body by exactly 1 is defined to have a magnitude of one Newton (I N). The direction of the force is the direction of the acceleration. It is a vector quantity. Thus, the net force on a body is the vector sum of all the forces acting on it. Some particular forces are described below:
1. Weight — is a force that pulls the body directly toward a nearby astronomical body; in everyday circumstances, that astronomical body is the earth. The force is primarily due to an attraction, called gravitational attraction, between the astronomical body and any object nearby. 2. Normal Force — is the perpendicular force (perpendicular to the surface) experienced by a body that is pressed against a surface, or pressed against another body. 3. Friction — is a force, which opposes the relative motion of a body at rest or in motion. 4. Tension — is the force exerted by a string, rope or cable on an object to which it is attached. A tension force pulls in the direction of the rope and is exerted uniformly along its entire length.
2.2 Mass Mass is a scalar quantity and is commonly known qualitatively as the amount of matter which an object is made. It is also defined as a measure of an object’s inertia. The greater an object’s mass, the greater its inertia and the less its motion changes when pushed or pulled by a force. 2.3 Newton’s Laws of Motion Sir Isaac Newton and his colleagues formulated three laws based on experimental observations which are called the laws of motion. The three laws of motion are as follows:
1. Newton’s First Law of Motion: The Law of Inertia A body at rest will remain at rest and a body in motion will continue to move in motion at constant velocity in a straight line unless, in either case, it is acted upon by an external unbalanced force. In an equation form, if then 2. Newton’s Second Law of Motion: The Law of Acceleration An unbalanced force acting on an object will cause the object to accelerate in the direction of the force. The acceleration is directly proportional to the vector sum of all the forces acting on the object and inversely proportional to the object’s mass. In equation form,
- Newton’s Third Law of Motion: The Law of Action and Reaction Forces Whenever one object exerts a force on another object, the second object exerts a reaction force of equal magnitude but in opposite direction to the first force.
- An unbalanced force of 50 N acts on an object weighing 100 N. What acceleration is produced? Solution:
- A constant horizontal force of 40 N acts on a body on a smooth horizontal surface. The body starts from rest and is observed to move 100 m in 5 s. a. What is the mass of the body? b. If the force ceases to act at the end of 5 s, how far will the body move in the next 5 s?
- Two inclined planes are arranged as shown below. The two bodies, 8 N and 10 N are tied at the ends of a cord that passes over a massless, frictionless pulley. Find a) the acceleration of the system, and b) the tension in the cord
Adding the two equations given above, we can solve for the acceleration. We find that:
2.5 Friction Friction opposes the motion of an object across a surface on which it rests and is directed parallel to the surface of the contact. There are two common types of friction: static friction and kinetic friction.
1. Static Friction — static frictional force exists when an object does not slide along a surface on which it rests even through a force is exerted to make it slide. If a large box is pushed but it does not slide, the
static frictional force resists the applied force. The force of friction in this case is called static because the box remains stationary. The maximum force that static frictional force exerts depends on two factors: a) The relative roughness of two surfaces in contact. Roughness is measured by the coefficient of static friction s. The larger the value of s, the rougher the surfaces and the harder it is to move the object. b) The magnitude of the normal force between the object and the surface on which it rests. The larger the normal force, the harder it is to make the object move.
2. Kinetic Friction — As an object slides across a surface, kinetic frictional force opposes its motion. The word kinetic signifies that the object is moving. In the case of a moving car, for example, the road exerts kinetic frictional force on the tires of the road. After an object, initially at rest, that is pushed or pulled, starts to move, less force is usually needed to keep the object sliding than the force required to make the object move. That is, kinetic frictional force is less than the maximum static friction. The effect of friction on the motion of an object is accounted for by defining a coefficient of kinetic friction, k, a number less than the coefficient of static friction. Properties of Frictional Force ✓ If a body remains stationary, the static frictional force fs , and the component of the applied force that is parallel to the surface are equal in magnitude but opposite in direction. If the component of parallel to the surface increases,, then fs also increases. ✓ The magnitude of fs has a maximum value that is equal to sN. That is, fs sN where N is the magnitude of the normal force. If the component of parallel to the surface exceeds sN , then the body begins to slide on the surface. ✓ Once a body begins to slide along a surface, the magnitude of the frictional force rapidly decreases to a smaller constant value given by fk = kN , where uk < us.
force 30 above the plane as shown, making the body move upward uniformly. Determine the magnitude of the applied force if the coefficient of kinetic friction between the surfaces in contact is 0.25.
- A 50 kg block rests on the floor. The coefficients of static and kinetic friction are 0.70 and 0.50, respectively. a) What is the minimum force needed to move the block? b) If the same force continues to push the block after it starts sliding, what will be its acceleration? Solution: a) The forces acting are as shown in the preceding page.
