3. What is the minimum work needed to push a 950-kg car 310 m up along a 9.0 incline? Ignore friction. Make sure you draw a free body diagram!

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1 Wor Problems Wor and Energy HW#. How much wor is done by the graitational force when a 280-g pile drier falls 2.80 m? W G = G d cos θ W = (mg)d cos θ W = (280)(9.8)(2.80) cos(0) W = W Mr. Kepple Name: Date: Period: 2. A 75.0-g firefighter climbs a flight of stairs 20.0 m high. How much wor is required? W climb = climb d cos θ W = (mg)d cos θ W = (75)(9.8)(20.0) cos(0) W = 4700 W = What is the minimum wor needed to push a 950-g car 30 m up along a 9.0 incline? Ignore friction. Mae sure you draw a free body diagram! P +y mg N θ + The minimum wor is when the car has constant elocity. Σ = 0 P mg sin θ = 0 P = mg sin θ W P = P d cos 0 W P = (mg sin θ) d W P = (950)(9.80)(30) sin 9.0 W P = W P A bo of mass 6.0 g is accelerated from rest by a force across a floor at a rate of 2.0 m/s² for 7.0 s. ind the net wor done on the bo. d = o t + 2 at2 d = at2 d = 2 at2 W = d cos θ W = (ma)( 2 at2 ) cos 0 W = 2 ma2 t 2 W = 2 (6.0)(2.0)2 (7.0) 2 W = 588 W 590

2 5. A 7,000-g jet taes off from an aircraft carrier ia a catapult. The gases thrust out from the jet s engines eert a constant force of 30 N on the jet; the force eerted on the jet by the catapult is plotted in the figure. Determine: (a) The wor done on the jet by the gases epelled by its engines during launch of the jet; and (b) the wor done on the jet by the catapult during launch of the jet. (a) Wor done by gases (b) Wor done by catapult W = d cos θ W = ( )(85) cos 0 W = W = 2 ( )(85) W = A 2200-N crate rests on the floor. How much wor is required to moe it at constant speed (a) 4.0 m along the floor against a drag force of 230 N, and (b) 4.0 m ertically? d (a) Along the floor (b) Vertically f N P W P = P d cos θ W = (230)(4.0)() W P = P d cos θ W P = mgd cos 0 P d mg W = 920 W P = (2200)(4.0)() W P = 8800 mg 7. At the top of a pole ault, an athlete pushes the pole with a force gien by ( ) = acting oer a distance of 0.20 m. How much wor is done on the athlete? 8. Calculate the amount of wor done by a force = 2 which acts on an object during its journey along the ais from = 0.0 to =.0 m. 0.2 W = d = ( )d 0 W = 2 d = d W = W = 75(0.2) (0.2)3 0 0 W = W = 2 2 ( 2) 0.0 W = 4( 0) W = 4.0

3 Wor-Energy Theorem Wor and Energy HW#2 Mr. Kepple Name: Date: Period:. The figure shows three forces applied to a trun that moes leftward by 3.00 m oer a frictionless floor. The force magnitudes are N, N, N, and the indicated angle is. During the displacement what is the change in inetic energy of the trun? W d cos θ ( )( ) cos W net W d cos θ ( )( ) cos 2 W + W + W W d cos θ ( )( ) cos 2. (a) How much wor is done by the horizontal force N on the 8-g bloc in the picture when the force pushes the bloc 5.0 m up along the 32 frictionless incline? (b) How much wor is done by the graitational force on the bloc during this displacement? (c) How much wor is done by the normal force? (d) What is the speed of the bloc (assume it was zero initially) after this displacement? (a) Wor done by P (b) Wor by graity (d) Speed of the bloc W P P d cos θ W P ( )( ) cos 2 W G W G G d cos θ mgd cos θ 2 m( 0 ) W W P 4 (c) Wor by normal force W N N d cos W G ( 8)( 8)( ) cos 22 W G W m 2( 4 7 4) ( 8) 4 82 m/s 4 m/s 3. At an accident scene on a leel road, inestigators measure a car s sid mar to be 98 m long. It was a rainy day and the coefficient of friction was estimated to be se these data to determine the speed of the car when the drier slammed on (and loced) the braes. N d μmgd m 0 f mg W 2μgd fd cos θ m( 0 ) μmgd cos 8 m( 0 ) 2( 8)( 8)( 8) 27 2 m/s 27 m/s

4 4. A 46.0-g crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. or the first.0 m the floor is frictionless, and for the net 0.0 m the coefficient of friction is What is the final speed of the crate after being pulled these 2.0 m? W W d cos d m( 0 ) W + W W d cos + fd cos 8 m( ) d + d μmgd W d μmgd 2 (d + d ) μmgd m 2 (22 )(2 ) ( 2)(4 )( 8)( ) (4 ) 2 8 m/s m/s 5. A mass is attached to a spring which is held stretched a distance by a force, and then released. The spring compresses, pulling the mass. Determine the speed of the mass when the spring returns: (a) to its normal length ( ); (b) to half its original etension ( /2). [Ignore friction] (a) Speed at (b) Speed at /2 W S W S 2 m( 0 ) m + m 2 2 m( 0 ) ()d / 2 m 2 / m () 2 m m

5 Chapter 7: Questions Wor and Energy HW#3 Mr. Kepple Name: Date: Period:. The figure shows two horizontal forces that act on a bloc that is sliding to the right across a frictionless floor. The graph shows three plots of the bloc s inetic energy ersus time. Which of the plots best corresponds to the following situations? ustify each response. (a) (b) (c) Graph 2. The forces on the bloc are balanced, which means no acceleration occurs. As a result, the inetic energy is constant. Graph 3. The net force points opposite to the direction of motion. The object will eentually come to rest and hae zero inetic energy. Graph. The net force points parallel to the direction of motion. The object will gain speed and the inetic energy will increase. 2. The figure shows four graphs (draw to the same scale) of the component of a ariable force (directed along an ais) ersus the position of a particle on which the force acts. Ran the graphs according to the wor done by the force on the particle from to, from most positie wor first to most negatie wor last. Ran: b, a, c, d. The wor done is the area under the cure. Graph (b) is the only graph with a net positie area. Graph (a) is net since it has a net area of zero. inally graph (c) and then (d) since graph (c) has less negatie area than graph (d). 3. Spring is stiffer than spring. The spring force of which spring does more wor if the springs are compressed (a) the same distance? ustify. Spring A. In order to compress each spring by an equal length, more force must be applied to the spring with the greater stiffness constant. As a result, the stiffer spring (spring A) does more wor. (b) by the same applied force? ustify. Spring B. When both springs are compressed by an equal applied force, the spring with the smaller stiffness constant will be compressed a greater distance and as a result more wor will be done.

6 4. In the figure, a greased pig has a choice of three frictionless slides along which to slide to the ground. Ran the slides according to how much wor the graitational force does on the pig during the descent, greatest first. ustify your raning. All tie. Since graity is a conseratie force, the wor done by graity will depend only on the initial and final height of the pig. Along each of the three paths shown the pig will start and end at the same height. Therefore the wor done by graity is the same along all three paths. 5. In three situations, a briefly applied horizontal force changes the elocity of a hocey puc that slides oer frictionless ice. The oerhead iews of the figure indicate, for each situation, the puc s initial speed, its final speed, and the directions of the corresponding elocity ectors. Ran the situations according to the wor done on the puc by the applied force, most positie first and most negatie last. ustify your raning. Raning: c, b, a. According to the wor-energy theorem, the wor done on the object is equal to the change in its inetic energy. Situation (c) is the only situation with positie wor since the object gains speed. Situations (a) and (b) both hae negatie wor since the puc loses speed. Kinetic energy is proportional to speed squared so more negatie wor is done in (a) since the magnitude of the speeds are greater than in (b). 6. The figure gies the component of a force that can act on a particle. If the particle begins at rest, what is its coordinate when it has (justify each response) (a) its greatest inetic energy? 3 m. The gain in inetic energy will be equal to the wor done, in other words the area under the cure. (b) its greatest speed? 3 m. Kinetic energy depends on speed. The location with the most inetic energy also has the most speed. (c) zero speed? m and m. The object starts at rest and returns to rest when the net wor done is equal to zero. The area under the cure from 0 m to 6 m is zero. (d) What is the particle s direction of trael after it reaches m? Negatie. The object returns to rest at 6 m and past this point is acted on by a negatie net force. It will accelerate and gain speed in the negatie direction.

7 Potential Energy Wor and Energy HW#4 Mr. Kepple Name: Date: Period:. A particular spring obeys the force law. (a) Is this force conseratie? Eplain. Yes this force is conseratie. Since the force is a function of position, the wor done by the force depends only on the initial and final position (the end points) of the object. Therefore, by definition, the force is conseratie. (b) Determine the form of the potential energy function. d ( a b ) d a 5 b5 C 2. The potential energy of an object is gien by ( ) (a) What is the force,? (b) What force acts on the object at m? () () d() d () (6 ) d d ( ) () 6 ( ) 6( ) ( ) 8 N 3. A particle constrained to moe in one dimension is acted on by the force ( ) where is a constant with units appropriate to the SI system. ind the potential energy function ( ), if is arbitrarily defined to be zero at m, so that ( ). d d d ( ) C ( ) C 8 C 8

8 4. The figure shows a plot of potential energy ersus position of a 2.0-g particle that can trael only along an ais. Assume nonconseratie forces are not inoled. Suppose the particle is released at with an initial speed of 7.0 m/s, headed in the negatie direction. Remember the wor-energy theorem! Since and this means that. In other words, when an object gains potential energy it loses inetic energy. (a) Does the particle hae enough inetic energy to reach m? K ( ) ( ) m ( )(7) 9 Yes the particle can reach. It needs at least 30 of inetic energy and it has 49. (b) What is the magnitude and direction of the force acting on the particle as it begins to moe to the left of m? d d N to the right 5. A spring has a spring constant of 82.0 N/m. How much must this spring be compressed to store 35.0 of potential energy? S S ( 5) A.60-m tall person lifts a.95-g boo off the ground so it is 2.20 m aboe the ground. What is the potential energy of the boo relatie to (a) the ground, and (b) the top of the person s head? boo (a) relatie to the ground (b) relatie to the head 6 head mgh mgh ( 95)(9 8)( ) ( 95)(9 8)( 6) ground 66 5

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