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physics_ch6homework - Chapter 6 Homework 1 An old oaken...

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Chapter 6 Homework 1. An old oaken bucket of mass 6.75 kg hangs in a well at the end of a rope. The rope passes over a frictionless pulley at the top of the well, and you pull horizontally on the end of the rope to raise the bucket slowly a distance of 4.00 m. (a) How much work do you do on the bucket in pulling it up? = w mg = W Fs = . . 6 75 kg9 8 ms2 =( . )( . ) 66 2 N 4 00 m = . 66 2 N = 265 J (b) How much work does gravity do on the bucket? = W . - . = - 66 2 N 4 00 m 265 J (c) What is the total work done on the bucket? = +- = Wtot 265 J 265 J 0 J 2. A tow truck pulls a car 5.00 km along a horizontal roadway using a cable having a tension of 850 N. (a) How much work does the cable do on the car if it pulls horizontally? If it pulls at 35.0° above the horizontal? Horizontally: = W Fs =( )( ) 850 N 5000 m = . × 4 25 106 J 35.0° above the horizontal: = W Fscosθ =( )( ) . ° 850 N 5000 m cos35 0 = . × 3 48 106 J (b) How much work does the cable do on the tow truck in both cases of part (a)? Horizontally: = W Fscosθ =( )( ) ° 850 N 5000 m cos180 =- . × 4 25 106 J 35.0° above the horizontal: = W Fscosθ =( )( ) ° 850 N 5000 m cos145 =- . × 3 48 106 J (c) How much work does gravity do on the car in part (a)? = °= W 850 N5000 mcos90 0 J Page | 1
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3. A factory worker pushes a 30.0-kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.25. (a) What magnitude of force must the worker apply? = = fk μkn μkmg = . . . 0 2530 0 kg9 8 ms2 = . 73 5 N (b) How much work is done on the crate by this force? = W Fs =( . )( . ) 73 5 N 4 5 m = . 330 8 J (c) How much work is done on the crate by friction? = W Fscosθ =( . )( . ) ° 73 5 N 4 5 m cos180 =- . 330 8 J (d) How much work is done on the crate by the normal force? By gravity? Normal Force: = . . °= W 73 5 N4 5 mcos270 0 J Gravity: = . . °= W 73 5 N4 5 mcos90 0 J (e) What is the total work done on the crate? = . - . + + = Wtot 330 8 J 330 8 J 0 J 0 J 0 J 4. Suppose the worker in Exercise 6.3 pushes downward at an angle of 30° below the horizontal. (a) What magnitude of force must the worker apply to move the crate at constant velocity? = Fy 0 = Fy 0 = + n mg Fsinθ = Fcosθ fk = + Fcosθ μkmg μkFsinθ = = + fk μkn μkmg μkFsinθ = - F μkmgcosθ μksinθ = . . . 0 2530 0 kg9 8 °- . ° ms2cos30 0 25sin30 = . 99 2 N (b) How much work is done on the crate by this force when the crate is pushed a distance of 4.5 m?
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