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04-203-08hwk-Ch5-6correct37

04-203-08hwk-Ch5-6correct37 - Chapter 5 Newton's Laws of...

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Chapter 5: Newton’s Laws of Motion 4. Picture the Problem : The billiard ball is accelerated along a straight line. Strategy: Find the acceleration from the initial and final speeds and from the time interval. Use the known acceleration to find the average force on the ball by using Newton’s Second Law. Solution: Determine the acceleration from the initial and final speeds, and apply Newton’s second Law: ( ) ( ) 3 12 m/s 0 0.53 kg 1600 N 1.6 kN 4.0 10 s – 0 v F ma m t - - Δ = = = = = Δ × Insight: This substantial force (about 360 lb) acts over a very short time, so the final speed isn’t all that spectacular. ----------------------------------------------------------------------------------------------------------------------------------------------------- 16. Picture the Problem : The force pushes on box 1 in the manner indicated by the figure at right. Strategy: The boxes must each have the same acceleration, but because they have different masses the net force on each must be different. These observations allow you to use Newton’s Second Law for each individual box to determine the magnitudes of the contact forces. First find the acceleration of all the boxes and then apply equation 5-1 to find the contact forces. Solution: 1. (a) The 7.50 N force accelerates all the boxes together: 1 2 3 1 2 3 2 ( ) 7.50 N 0.798 m/s 1.30 kg 3.20 kg 4.90 kg F F m m m a a m m m a = + + = + + = = + + 2. Write Newton’s Second Law for the first box: ( ) ( ) c12 1 2 c12 1 7.50 N 1.30 kg 0.798 m/s 6.46 N F F ma F F ma = - = = - = - = F arrowrightnosp 3. (b) Write Newton’s Second Law for the third box: ( ) ( ) 2 c23 3 4.90 kg 0.798 m/s 3.91 N F m a = = = = F arrowrightnosp Insight: Another way to solve the problem is to note that c12 F accelerates boxes 2 and 3: ( ) ( ) 2 c12 3.20 4.90 kg 0.798 m/s 6.46 N F = + = , the same result as in step 2. 23 . Picture the Problem : The two teenagers pull on the sled in the directions indicated by the figure at right. Strategy: Write Newton’s Second Law in the x direction (parallel to a arrowrightnosp ) in order to find the acceleration of the sled. Solution : Write Newton’ s Second Law in the x direction ( ) ( ) sled child sled child 2 2 cos 35 57 N 2 cos35 57 N 2 55 N cos35 57 N 1.5 m/s 19 3.7 kg x x x x F F m m a F a m m a = °- = + °- = + °- = = + Insight: Some of the force exerted by the teenagers is exerted in the y direction and cancels out; only the x components of the forces move the sled.
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----------------------------------------------------------------------------------------------------------------------------------------------------- 29. Picture the Problem : The suitcase is accelerated straight upward by the applied force. Strategy: There are two forces acting on the suitcase, the applied force F arrowrightnosp acting upward and the force of gravity W arrowrightnosp acting downward. Use Newton’s Second Law together with the known acceleration to determine the mass and weight of the suitcase. Let upward be the positive direction.
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