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PhysicsCh3

PhysicsCh3 - 1 Two forces act at a point object as follows...

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1. Two forces act at a point object as follows: 100N at 170.0 degrees and 100N at 50.0 degrees. Find their resultant. The x-component is 100cos50.0 100cos170.0 34.202 34.2 o o x F N = + = - = - The y-component is 100sin50.0 100sin170.0 93.969 94.0 o o y F N = + = = The resultant is ( 29 ( 29 2 2 2 2 34.202 93.969 100 x y F F F N N N = + = - + = 1 1 0 93.969 180 tan 180 tan 110 34.202 y o o x F N F N θ - - = + = + = - 2. Compute algebraically the resultant of the following coplanar forces: 100N at 30 degrees, 141.4N at 45 degrees and 100N at 240 degrees. The x-component is 2 100cos30 141.4cos45 100cos240 136.59 1.4 10 o o o x F N = + + = = × The y-component is 100sin30 141.4sin 45 100sin 240 63.382 63 o o o y F N = + + = = The resultant is ( 29 ( 29 2 2 2 2 2 2 1.4 10 63 1.5 10 x y F F F N N N = + = × + = ×

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1 1 0 2 63.382 tan tan 24.893 25 1.5 10 y o x F N F N θ - - = = = = × 3. A 12.0g bullet is accelerated from rest to a speed of 700 m/s as it travels 20.0 cm in a gun barrel. Assuming the acceleration to be constant, how large was the accelerating force? 2 1 2 o x v t at = + o v v at = + Since the bullet is accelerated from the rest then v o = 0. Then 2 1 (1) 2 (2) x at v at = = From (2) v t a = Substitute this in (1): 2 2 1 2 2 v x a a v x a = = Then the acceleration of the bullet is
2 2 v a x = By Newton’s second law the accelerating force is 2 2 4 2 (0.012 )(700 / ) 14700 1.47 10 2(0.200 ) mv F ma x kg m s F N m = = = = = × 4. A 700N man stands on a scale on the floor of an elevator.

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