Example 4.1 An Acceilerating Hockey Puck A hockey puck having a mass of 0.30 kg

Question

Example 4.1 An Acceilerating Hockey Puck A hockey puck having a mass of 0.30 kg slides on the frictionless, horizontal surface of an ice rink. Two hockey sticks strike the puck simultaneously, exerting the forces on the puck shown in the figure. The force F1 has a magnitude of 4.9 N, and the force F, has a magnitude of 8.0 N. If, 20° and 2·57", determine both the magnitude and the direction of the puck's acceleration. Conceptualize Study the figure. Using your expertise in vector addition from the chapter, predict the approximate direction of the net force vector on the puck. The acceleration of the puck will be in the same direction. A hockey puck moving on a trictioniess surface Categorize Because we can determine a net force and we want an acceleration, this problem is categorized as one that may be solved using Newton's second law Analyze Find the component of the net force acting on the puck in the x direction: (4.9 N) (0.940) + (8.0 NX0.545) 9.0 N Find the component of the net force acting on the puck in the y direction: ',+5sin (-20.) + F, sin 57. . (4.9 N) (-0.342) + (8.0 N)(0.839)-5.0 N Use Newton's second law in component form to find the x and y components of the puck's acceleration: m 0.30 kg Find the magnitude of the acceleration a-(30 m/s (17 m/s 34.48 m/s Find the direction of the acceleration relative to the positive x axis: 30 8-12953 Finalize The vectors in the figure can be added graphically to check the reasonableness of our answer Because the acceleration vector is along the direction of the resultant force, a drawing showing the resultant force vector helps us check the validity of the answer (Ciryi HINTS: GETETING STARTED IMSTUCK Suppose three hockey sticks strike the puck simultaneously, with two of them exerting the forces from the example above. The result of the three forces is that the hockey puck shows no acceleration. What must be the components of the third force? 7.5 Use the methods and results of the Exercise and find the additional force from the third hockey stick needed to reduce the acceleration to zero. Need Help?

Explanation / Answer

F1 = 4.9 (cos20 i - sin20j)

F1 = 4.60 i - 1.68 j N

F2 = 8 (cos57 i + sin57 j)

F2 = 4.36 i + 6.71 j

if there is no acceleration then net force will be zero.

Fnet = F1 + F2 + F3 = 0

F3 = - 8.96 i - 5.03 j

F3x = - 8.96 N

F3y = - 5.03 N

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