Work and Energy Problems

Transcription

1 orce F o trength 0N act on an object o a 3kg a it ove a ditance o 4. I F i perpendicular to the 4 diplaceent, the work done i equal to: Work and Energy Proble a) 0J b) 60J c) 80J d) 600J e) 400J Since the Force i perpendicular to the diplaceent, there i no work done by thi orce. Under the inluence o a orce, an object o a 4kg accelerate ro 3 / to 6 / in 8. ow uch work wa done on the object during thi tie? a) 7J b) 54J c) 7J d) 96J e) an not be deterined ro the inoration given Thi i a job or the work energy theore. bo o a lide down a rictionle inclined plane o length L and vertical height h. What i the change in gravitational potential energy? a) -gl b) -gh c) -gl/h d) -gh/l e) -ghl The length o the rap i irrelevant, it i only the change in height W K v vi 4 kg J n object o a i travelling at contant peed v in a circular path o radiu r. how uch work i done by the centripetal orce during one-hal o a revolution? a) πv J b) πv J c) 0J d) πv r J e) πv /r J Since centripetal orce alway point along a radiu toward the centre o the circle, and the diplaceent i alway along the path o the circle, no work i done. While a peron lit a book o a kg ro the loor to a tabletop,.5 above the loor, how uch work doe the gravitational orce do on the block? a) -30J b) -5J c) 0J d) 5J e) 30J The gravitational orce point downward, while the diplaceent i upward W gh kg J

2 block o a 3.5kg lide down a rictionle inclined plane o length 6 that ake an angle o 30 o with the horizontal. I the block i releaed ro ret at the top o the incline, what i the peed at the botto? orce o 00N i required to keep an object at a contant peed o / acro a rough loor. ow uch power i being epended to aintain thi otion? a) 4.9 / b) 5. / c) 6.4 / d) 7.7 / e) 9. / The work done by gravity i equal to the change in Kinetic Energy. W K gh v vi gh v v gh 9.8 in a) 50W b) 00W c) 00W d) 400W e) annot be deterined with given inoration Ue the power equation P Fv 00N 400W otorcycle peed up ro ret, what type o energy i converted into Kinetic energy? Quetion Linda i pulling her wagon behind herel. She eert a orce o 00 N along a rope at an angle o 0 o to the horizontal. ow uch work did he do to pull the wagon 30? a) Theral b) heical Energy c) Nuclear d) Elatic e) Gravitational Potential energy Work =orce ditance 0 W Fd co 00N30 co J Quetion truck ove with velocity v 0 = 0 / on a lick road when the driver applie the brake. The wheel lide and it take the car 6 econd to top with a contant deceleration. a) ow ar doe the truck travel beore topping? b) Deterine the kinetic riction between the truck and the road. Solution to Quetion truck ove with velocity v 0 = 0 / on a lick road when the driver applie the brake. The wheel lide and it take the car 6 econd to top with a contant deceleration. a) ow ar doe the truck travel beore topping? b) Deterine the kinetic riction between the truck and the road. d v0 v t

3 Solution to Quetion truck ove with velocity v 0 = 0 / on a lick road when the driver applie the brake. The wheel lide and it take the car 6 econd to top with a contant deceleration. a) ow ar doe the truck travel beore topping? b) Deterine the kinetic riction between the truck and the road. Eaple n object o a.0 kg travelling at 5.0 / enter a region o ice where the coeicient o kinetic riction i 0.0. Ue the Work Energy Theore to deterine the ditance the object travel beore coing to a halt. Firt we need the acceleration the car eperience. v a t Since the only acceleration orce eperienced by the car i riction F F a a uf n a ug a ug a u g kg Solution n object o a.0 kg travelling at 5.0 / enter a region o ice where the coeicient o kinetic riction i 0.0. Ue the Work Energy Theore to deterine the ditance the object travel beore coing to a halt. F N Force We can ee that the object weight i balanced by the noral orce eerted by the ice. Thereore the only work done i due to the riction acting on the object. Let deterine the riction orce. F u F k N ukg 0.0.0kg N Now apply the work Energy Theore and olve or d W KE F F d v vi 3 g 0.98N d.0kg 0.0kg 5.0.5J d 0.98N In a perect world a.0 kg ball i dropped ro.0 and all the energy i converted E M = Ep + Ek ro potential to E kinetic M al = gh + ½ v o each tie the ball = bounce 0 J + it 0 J reache = it 0 original J height. ) Find the velocity o the ball ater the irt drop a the ball reache the ground? ouncing all E M = Ep + Ek E MTop = gh + ½ v v = 0 / at the top. =.0 kg (9.8 / ) () = 0 J ey What would the kinetic energy be halway down? E M otto = Ep + ½ v 0 J = ½ (.0kg) v 0J 0J v v kg. 0kg What peed will a 00g baeball reach when dropped ro a height o.0? Would the peed change i the ball wa bowling ball (5.0kg)? V E = 0 / M EP EK E E h = 0 Given: = 00 g = 0.00kg h =.0 h = 0 g = 9.8 / v = 0 / MTOP MOTTOM EP EK EP EK gh v gh v gh v v 63. gh v v Energy Eiciency Energy Eiciency = E out E in 00% Energy In (input) - the energy put into the yte to do work uch a gaoline or a car or electrical energy or an elevator. Energy Out (output) = the ueul energy that reult 3

4 E. irely ha 4.3 J o cheical ood energy that i converted to 3.63 J o glowing radiant energy. What i the ly eiciency o it energy tranoration? Given: E out = 3.63 J E in = 4.3 J E E = E out E in 00% = 3.63 J 4.3 J 00% = 88 % E. What i the eiciency o a rope and pulley yte i a painter ued.93 kj o echanical energy to pull on the rope and lit a 0.0 kg paint barrel at a contant peed to a height o 7.5? Given: E =. 93 kj = 930 J h = 0 h = 7.5 = 0.0 kg g = 9.8 / ΔEp = W net ΔEp = gh = 0.0kg(9.8/)(7.5) = 470 J % E e = E out E in 00% = 470 J/ 930 J 00% = 76% ollective Energy: Power in Nuber??? (or un) Vauce: Powerul Quetion ow uch power doe a wier produce i he tranor.4 kj o cheical energy into kinetic and theral energy in.5? Δ E = 400 J Δ t =.5 P =? P = ΔE / Δt = 400 J /.5 = 9 W n elevator and it occupant have a a o 300.0kg. The elevator otor lit the elevator to the th loor, a ditance o 40.0 in What i the average power output o the otor? Given: = 300 kg h = 40.0 g = 9.8 / Δt = 74.8 P = ΔE / Δt = gh / Δt = (300.0kg)(9.8/)(40.0) 74.8 = 680 J/ = 680 W What i the cot o operating a 60.0 W light bulb 4.0 hour a day or 6.0 day i the price o electrical energy i $0.3/kWh? kwh = 000 W h ΔE = P Δt h = 4.0 h/day 6.0 day E = 60.0 W 4 h = 440 Wh =.44 kwh = 4h ot =.44 kwh 0.3/kWh = $0.87 = $0.9 4

5 n Energy Quetion kg ball all ro ret and looe 0J o Gravitational Potential Energy. ow ar did the ball all? Ue the Gravitational Potential Energy Equation U g gh 0J kg 9. 8 N h kg 0J h. 0 N kg 9. 8 kg Intereting Quetion bo o a 0 kg i puhed at a contant peed o 5 / [E] along a urace where the coeicient o kinetic riction i unknown. When the applied orce i reoved, the bo i allowed to lide on it own until it coe to ret. Deterine the coeicient o kinetic riction i the bo lid a ditance o.0 ater the applied orce i reoved. We can olve thi proble in two dierent way: Energy or Dynaic. Intereting Quetion bo o a 0 kg i puhed at a contant peed o 5 / [E] along a urace where the coeicient o kinetic riction i unknown. When the applied orce i reoved, the bo i allowed to lide on it own until it coe to ret. Deterine the coeicient o kinetic riction i the bo lid a ditance o.0 ater the applied orce i reoved. Intereting Quetion bo o a 0 kg i puhed at a contant peed o 5 / [E] along a urace where the coeicient o kinetic riction i unknown. When the applied orce i reoved, the bo i allowed to lide on it own until it coe to ret. Deterine the coeicient o kinetic riction i the bo lid a ditance o.0 ater the applied orce i reoved. Uing Kinetic Energy Theore. Uing Dynaic and kineatic. KE Work done by Friction v vi Frictiond 0 0kg 5 gd N 5J 0kg 9. 8 kg 5J 96J F F riction a a g a a g Kineatic. v v ad i 0 5 a a 6. 5 Eaple bo o a 5kg i releaed ro ret at point, the top o a long rictionle lide. Point i at height 0 above the level point and. lthough the lide i rictionle, the horizontal urace ro point to i not. The riction Force between the bo and thi urace i N, and the horizontal ditance between point and i 3. a) Find the peed o the bo when it height above the ground i / b) Find the peed o the bo when it reache. c) Deterine the work done by riction between and. d) Deterine the peed o the bo when it reache e) I the lide wa not rictionle, deterine the work done by riction a the bo oved ro to i the peed at wa ½ o the peed calculated in b) Eaple bo o a 5kg i releaed ro ret at point, the top o a long rictionle lide. Point i at height 0 above the level point and. lthough the lide i rictionle, the horizontal urace ro point to i not. The riction between the bo and thi urace i N, and the horizontal ditance between point and i 3. a) Find the peed o the bo when it height above the ground i / E U K g 0 g total G U K E G total v g v g g v g v U k. 5

6 Eaple bo o a 5kg i releaed ro ret at point, the top o a long rictionle lide. Point i at height 0 above the level point and. lthough the lide i rictionle, the horizontal urace ro point to i not. The riction between the bo and thi urace i N, and the horizontal ditance between point and i 3. b) Find the peed o the bo when it reache. Eaple bo o a 5kg i releaed ro ret at point, the top o a long rictionle lide. Point i at height 0 above the level point and. lthough the lide i rictionle, the horizontal urace ro point to i not. The riction Force between the bo and thi urace i N, and the horizontal ditance between point and i 3. c) Deterine the work done by riction between and E U K g 0 g total G U K E G total 0 v g v g v g v W F d W N 3 6J ey, note that the work done by riction i negative, it took away 6J o energy. Eaple bo o a 5kg i releaed ro ret at point, the top o a long rictionle lide. Point i at height 0 above the level point and. lthough the lide i rictionle, the horizontal urace ro point to i not. The riction Force between the bo and thi urace i N, and the horizontal ditance between point and i 3. d) Deterine the peed o the bo when it reache. K 6J K g 6J v 5kg J 5kg v kg v 484J.5 v 93.6 L Why, ue gh or K? v 3.9 Eaple bo o a 5kg i releaed ro ret at point, the top o a long rictionle lide. Point i at height 0 above the level point and. lthough the lide i rictionle, the horizontal urace ro point to i not. The riction Force between the bo and thi urace i N, and the horizontal ditance between point and i 3. e) I the lide wa not rictionle, deterine the work done by riction a the bo oved ro to i the peed at wa ½ o the peed calculated in b) U K W U K U K W v g 0W g g g W 4 g 3 W g g W 5 kg W 367.5J 6