Composition of Forces
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Composition of Forces

In the study of motion, there are two quantities we should understand, these are the scalar and vector quantities. A scalar quantity is described by its magnitude only while a vector quantity has both magnitude and direction. Force, velocity, acceleration, displacement and electric field are vector quantities. Speed, distance, mass, volume, time density are some examples of scalar quantities.
Theory: Force is defined as a push or a pull. It is a vector which means it has a magnitude and direction. A body may be acted upon by two or more forces which move in the same or opposite directions. The sum of the forces is called the resultant. When one or more forces act upon an object at rest, and their resultant is not zero, the body will be set into motion. Considering that forces are vector quantities, they can be resolved into components. There are several situations in which force vectors are resolved into two components, one parallel to the surface and the other perpendicular to it. The parallel component tends to make the car roll downhill, and the perpendicular component deforms the board. The vectors are added by the tail of one vector at the head of the other vector. Neither the direction nor the length of either vector is changed. Once this is done, a third vector is drawn. This connects the tail of the first vector to the head of the second vector. This resulting vector now represents the sum of two vectors, it is called the resultant. Two or more forces which are acting at a point can be combined into an equivalent single force. This single equivalent force is called the resultant of the force. The method of solving for the resultant is known as composition of force. The single force which can balance two or more forces acting at a point is called the equilibrant of the forces. Forces are vector quantities. To specify a force, both its magnitude and its direction must be given. A force may therefore be represented by an arrow; the length of the arrow represents, the magnitude of the force according to a chosen scale, and the direction of the arrow represents the direction of the force. Objective: To determine the direction of the resultant force of a simple force system. Materials: Spring scales (3), meter stick, pencil, set of weights, toy car, string Procedure: Part A. 1. Link the two spring scales. Slowly pull them apart. 2. Record the reading on the scale. 3. Combine the spring scales and hook them to a third scale. 4. Pull the scale slowly and write down the readings. Part B. 1. Add equal weights to both ends of the toy car on top of the table. 2. Observe what happens when you release the toy car. 3. Add 100 grams to one end and holding the toy car on the middle of the table, let the car go. Write down your observations. Diagrams: Observations: Questions and Problems: 1. In physics, why is the knowledge of vector important? 2. Differentiate vector quantities from scalar quantities. Give examples each. 3. Why is it necessary to place the arrow head of the vector in the terminal point? 4. Draw the vector diagram of the following: a) A box is acted upon by the force: 300 NEWTONS to the right and 400 NEWTONS upward. What is the resultant force acting on the box? b) A boat with a speed of 6 m/sec is moving against the water current with a speed of 2m/sec. What is the resultant velocity of the boat? 5. Two vectors are 8 and 12 units long. The first vector is towards west and the second is directed 70oN of W. Using the law of cosine, find the resultant. 6. Describe and compare the participants of the two teams in the tug-of-war game. Prepared by: Jessie R. Agudo, BSCE/M.A.T. Mathematics

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