Vector Addition OBJECTIVE Upon completion of this lab, the student will be able
ID: 1654375 • Letter: V
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Vector Addition OBJECTIVE Upon completion of this lab, the student will be able to add vectors by using both analytical (method of component) and graphical (head-to-tail) methods and understand how vectors are used in physics. EQUIPMENT LIST Available in the room . Chalk Sensitive scale Available at each table Double meter stick L-shaped metal ruler Large protractor Force table with 3 pulleys . Ring with three strings .Mass set with hangers · INTRODUCTION Vectors are quantities that have both magnitude and direction and do not add like the numbers you are accustomed to. Vectors can be used to describe both static properties, such as positions and forces, or can be used to describe dynamic properties, such as velocity and acceleration. As you may recall, force is a vector quantity, i.e. to fully specify a force you must identify both its magnitude and its direction. For example, a vector in the x-y plane can be fully described if we specify its length and the angle it makes with either axis. Alternatively, the same vector can be fully described if we know its components (or projections) along the two axes (see figure). ty r cos It is easy to show that the angle can be obtained from the components by applying some elementary trigonometry. Since the tangent of an angle is defined as tan = (side opposite to ) / (side adjacent to it follows, using the vector components rx and ry (see figure), that e-tan"() tane- then (tan is called the inverse tangent, or arc-tangent).Explanation / Answer
Ans)
x-components of both F1 and F2:
F1cos20 + F2cos150 = 0.1*9.8*0.94 + 0.15*9.8*(-0.86) = -0.343 N (-ve sign means direction is -x)
y compoents:
F1sin20 + F2sin150 = (0.1*9.8*0.34) + (0.15*9.8*0.5) = 1.068 N
Fr = sqrt(Fx^2 + Fy^2 ) = 1.122 N
tan(theta) = Fy/Fx = 1.068/-0.343 = -3.113
theta = 72.19o
part b) MAgnitude = -1.122
direction = 180+72.19 = 252.19o(since it will be directly opposite)
part c)
Just draw the x and y components of all the forces on a graph paper and equate x comopents and y components seperately to get values as we got above.
If you want me to draw this too let me know in comment section
Hope it helps :)
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