Physic105 the force vectors

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timer Asked: Feb 1st, 2021

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I'm working on a physics case study and need a sample draft to help me understand better.

can you help answer those questions and I already uploaded the file in below. thank you!

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FORCE VECTORS Purpose The purpose of this experiment is to familiarize the student with some elementary vector concepts and to determine the resultant of some concurrent, coplanar forces. Theory A vector is a quantity that has both magnitude and direction. For instance, a force of 10 lb upward or a velocity of 30 miles per hour east is a vector. A scalar is a quantity that has magnitude but not direction. For instance, temperature and volume are scalars, since it would make no sense to speak of a temperature of 70 °F west or a volume of 20 cubic feet south. The resultant of two or more vectors is the single vector that could be substituted for the given vectors and have the same effect. Although there are many types of vectors, this experiment will concentrate on force vectors and their resultants. Suppose that a 3 lb force is acting on a body in an easterly direction and a 2 lb force is acting on the body in a north-easterly direction as in Figure la. The 3 lb force by itself would cause the body to accelerate toward the east; and the 2 lb force by itself would cause the body to accelerate toward the northeast. If both of these forces (and only these two forces) act on the body, the body will accelerate in an intermediate direction as shown. A single force R could produce the same acceleration. See Figure lb. Since R is a single vector having the same effect as the given vectors, R is the resultant of the given vectors. Figure 1 Resultant of Two Forces The magnitude and direction of the resultant of two given vectors can be predicted theoretically by drawing a parallelogram to scale. This technique is demonstrated in Figure 2 for the forces previously described. In the absence of other drafting tools, the parallelogram can be constructed with a compass and ruler as shown in Figure 3. Figure 2 Resultant by the Parallelogram Method Often, several forces act on a body and cancel each other out, so that the body remains in equilibrium. A body is said to be in mechanical equilibrium if it is remaining at rest or if it is moving in a straight line at a constant speed. This experiment will be restricted to the case of a body at rest under the action of three concurrent, coplanar forces. (By “concurrent" forces, it is meant that their lines of action intersect at a single point when extended. This condition insures that the forces do not cause the body to rotate. By "coplanar" forces, it is meant that they lie in a single plane. This restriction permits a simpler analysis.) Figure 4 is a sketch of the force-board apparatus to be used in this experiment. Three spring balances apply three forces to a metal ring near the center of the force board. The balances tend to adjust themselves, so that the metal ring comes to rest and remains at rest. The chains attached to the spring balances can be fastened to the slots in various ways to provide some control over the magnitudes and angles of the forces. Figure 5 is a vector diagram of the three forces acting on the ring of the force board. The resultant of all three forces must be zero, if the ring is to remain at rest. Let us begin by finding R 12, the resultant of F1, and F2, as shown in Figure 6. R12 can be substituted for F1, and F2, as shown in Figure 7; and the effect should be the same. Thus, R12 and F3 in Figure 7 are equivalent to the original three forces. If R 12 and F3 are to cancel each other out in their effect on the ring, they must be equal and opposite. F3 can be called the equilibrant of F1 and F2, since it permits the ring to remain in equilibrium while being acted upon by F1 and F2. In general, the equilibrant must be equal in magnitude and opposite in direction to the resultant of all other forces acting on the body. Experiment: Helpful site: https://www.mathsisfun.com/algebra/vectors.html Objectives: • • 1. The student will be able to differentiate between scalar quantities and vector quantities. The student will be able to resolve vectors into its components. Classify the following quantities to either scalar quantity or vector quantity by highlighting the correct answer: Weight Scalar Speed Scalar Mass Scalar Acceleration Scalar Vector Vector Vector Vector Density 2. Scalar Vector Distance Scalar Vector Force Scalar Vector Volume Scalar Vector Find the magnitude and direction of the resultant force of F1 and F2 by filling the table. The magnitudes and directions of F1 and F2 are given. Force Magnitude of force Direction (θ) XYcomponent component F1 44 28 F2 17 106 Resultant The magnitude of the resultant force is: The direction of the resultant force is: 3. Find the magnitude and direction of the resultant force of F1, F2, and F3 by filling the table. The magnitudes and directions of F1, F2, and F3 are given. Force Magnitude of force Direction (θ) X - component Y - component F1 0.77 100 F2 0.61 30 F3 0.43 156 Resultant The magnitude of the resultant force is: The direction of the resultant force is: 4. Vectors addition using PhET Interactive Simulations: https://phet.colorado.edu/sims/html/vector-addition/latest/vector-addition_en.html Consider vector 𝑎⃗ and vector 𝑏⃗ are force vectors, and vector 𝑐⃗ is the resultant vector. a. b. c. d. e. f. g. h. i. j. Click on the link shown above and select “Explore 2D” option window at the bottom of the graph. Drag the origin of the graph paper to the middle. Click on vector segment 𝑎⃗ and drag it so the tail positioned at the origin of the graph. Adjust vector 𝑎⃗ to a magnitude 6 N, and the angle θ = 30.0˚. Drag vector segment 𝑏⃗ to the graph so the tail at the origin. Adjust vector 𝑏⃗ so the magnitude is 5 N, and the direction with angle θ = 90.0˚. Add the two vectors graphically using the head to tail method. Click on the sum vector where 𝑠⃗ = 𝑎⃗ + 𝑏⃗ . Write the magnitude and the direction of the sum vector (resultant) 𝑠⃗ . Use the magnitudes and directions of the added vectors to calculate the magnitude and direction of the resultant vector 𝑠⃗ using the analytical method. Magnitude of vector Direction (θ) 𝑎⃗ 6 30 𝑏⃗ 5 90 Vector 𝑠⃗ X- component Y- component What is the magnitude and direction of vector 𝑠⃗ ? To make the system at equilibrium, an equilibrant force 𝐹𝐸 should be applied, what is the magnitude and direction of 𝐹𝐸 ? 5. Calculate the magnitude and direction of the resultant force of the forces given in the figure below: 6. What is the relation between the resultant force and the equilibrant force? ...
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