In the super market, Gabby pulls her grocery cart by exerting a force F, shown in the Figure below. 55" (20.0 N) +x 8. Which one of the following diagrams correctly shows the x and y component-vectors of the force F? +y B) A) C) 55° 55° 55° (20.0 N) (20.0 N) (20.0 N) +x +x +x D) E) 55 55 (20.0 N) (20.0 N) +x +x
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- As shown in the attached figure below, three force vectors act on an object. The magnitudes of the forces are F1= 80.0 N, F2 = 60.0 N, and F3 = 40.0 N, where N is the standard SI unit of force. The resultant force acting on the object is given by A. 40.0 N at an angle 60.0° below +x-axis B. 60.0 N at an angle 90.0° above +x-axis C. 20.0 N at an angle 34.3° below +x-axis D. 180 N at an angle 60.0° below +x-axis E. 35.5 N at an angle 34.3° above +x-axisVector F₁ = 625 N makes an angle of 2700 when rotated counterclockwise from the +x axis. Vector F2 = 875 N makes a 1200 angle from Vector F₁ when rotated counterclockwise. What is the magnitude a vector needed to balance the two forces? O 680.6 N O86.2 N -980.6 N O-670.6 N O980.6 N 78.2 N O 580.6 N 780.6 N20 N y 57 N TF₂ 45° 50 N F 15° What is the net force: Fnet F₁ + F₂ + F3. Write your answer as a magnitude and an angle to indicate direction (Newtons, degrees from positive x-axis). =
- Determine the magnitude of the x- component of force Q (in N) if P=96.4 N, Q = 55.2 N , 0= 55.53° and a = 49.46°.Round off only on the final answer expressed in 3 decimal places. Instead of units, indicate the direction of the x-component. Use R if to the right, L if to the left, U if upward or D if downward. y PThe helicopter view in the figure below shows two people pulling on a stubborn mule. (Take F₁ = 137 N and F₂ = 74.0 N.) 75.0° direction 60.0⁰ x (a) Find the single force that is equivalent to the two forces shown. 149.56 magnitude Your response differs from the correct answer by more than 10%. Double check your calculations. N 23.65 X Your response differs from the correct answer by more than 10%. Double check your calculations. counterclockwise from the +x-axis (b) Find the force a third person would have to exert on the mule to make the net force equal to zero. magnitude N direction counterclockwise from the +x-axisVECTOR ADDITION: Find the sum of two ‘forces’: 100 g at 30º and 200 g at 120º, by: A) Graphical Method: Make the X- and Y-axes. Use a scale of 25 g = 1.0 cm. Draw arrows of appropriate lengths at 30º and 120º, both starting from the origin. Add them using the Parallelogram method. Measure the length and angle of the resultant. Convert length to magnitude of the resultant vector using the scale used to draw the vectors. Record the results in the Data Table. B) Analytical Method: Compute the sum of the two vectors by using the Component Method (Ax = A cosθ and Ay = A sinθ ) as well as the Triangle Method (A/Sin α = B / Sin β = C / Sin γ and C2 = A2 + B2 – 2AB Cos γ). Record the results in the Data Table.
- Determine the resultant force of forces F₂ and F3 as a cartesian vector. Note that the angles shown in the force F2 are the coordinate angles a, B and y with respect to the coordinate axes. 55⁰ F₁ = 100 lb 65⁰ 120° 55° 35⁰ F₁ = 400 lb F₂ = 600 lbConsider a w-N weight suspended by two wires as shown in the accompanying figure. If the magnitude of vector F2 is 100 N, find w and the magnitude of vector F1. 40° 35° F, F2consider a force vector = 300 g at the 40º angle. resolve this vector into its x- and y-components by the following methods: a) graphical: make the x- and y-axes. use a scale of 30 g = 1.0 cm, and draw an arrow of appropriate length at 40º. drop perpendiculars from the tip of the vector to the x- and y-axes. measure the lengths of these lines and hence find the magnitudes of fx and fy. (do not calculate using trigonometry) record the results. b) analytical: compute the magnitudes of fx and fy by using the component method (equations 3-3 and 3-4). record the results.
- 5N Knot 120° 3N 12. The figure above shows three ropes tied together in a knot. One of your friends pulls on a rope with a force of 3 Newtons and another pulls on a second rope with a force of 5 Newtons. How hard and in what direction must you pull on the third rope to keep the knot from moving? (Hint: If you don't want the knot to move, the net force must be zero.)P. B. 2. Given: P = 334 N and Q = 405 N Angle A = 30 degrees Angle B = 18 degrees Angle C= 51 degrees Angle D = 20 degrees Solve for the magnitude of the resultant of the two forces.Vector Addition of Nonperpendicular Forces Problem: 1. A force of 40N and a force of 60 N act concurrently on a point P. The 60 n force acts in the direction of due east. The 40 n force acts in the direction 60° north of east. What is the magnitude and direction of their resultant? 2. A 100 N force and a 50 N force act on a point P. The 100 n force acts due north. The 50 N force acts due east. What is the magnitude and direction of the resultant force?