(0.3 kg) and m 2. has moved a distance of 0.4 m.

Transcription

1 Energy - Unit 5.2B- Problem 5.1B m 2 Masses m 1 (0.3 kg) and m 2 (0.8 kg) are connected by a massless string which passes over a massless pulley. If the masses are released from rest, find the speed of the masses at the instant that m 2 has moved a distance of 0.4 m. m Using the language of energy, describe in a single sentence the energy conversion process as the two masses move from their initial positions to the positions of interest in the problem. m 2 m 1 Workbook for Introductory Mechanics Problem-Solving Copyright by Daniel M. Smith, Jr. Sponsored by FIPSE (U.S. Department of Education)

2 5 134 Energy - Unit 5.2B - Problem 5.1B m 2 Masses m 1 (0.3 kg) and m 2 (0.8 kg) are connected by a massless string which passes over a massless pulley. If the masses are released from rest, find the speed of the masses at the instant that m 2 has moved a distance of 0.4 m. m The GPE of m 1 plus the GPE of m 2 are converted to the new GPE of m 1 plus the new GPE of m 2 plus the KE of m 1 plus the KE of m 2. Compare this statement with the bar graphs of frame

3 Energy - Unit 5.2B - Problem 5.2B A roller-coaster car of mass 480 kg is raised to an initial height of 18.0 m above ground level. With a speed of 1.3 m s the car begins its descent. (a) Ignoring friction, what is the car s speed when it reaches a horizontal section of track of height 4.0 m above ground level? The car ascends its first hill to reach a level of 8.5 m above ground. (b) What is the car s speed at this level, again ignoring friction? (c) If the car s speed after ascending the hill is actually 10.1 m s, how much energy has been lost from the start because of the friction between the track and the coaster car? For part (a), use the language of energy to describe, in a single sentence, the energy conversion process as the roller coaster car moves from A to B. A B ground Workbook for Introductory Mechanics Problem-Solving Copyright by Daniel M. Smith, Jr. Sponsored by FIPSE (U.S. Department of Education)

4 5 136 Energy - Unit 5.2B - Problem 5.2B A roller-coaster car of mass 480 kg is raised to an initial height of 18.0 m above ground level. With a speed of 1.3 m s the car begins its descent. (a) Ignoring friction, what is the car s speed when it reaches a horizontal section of track of height 4.0 m above ground level? The car ascends its first hill to reach a level of 8.5 m above ground. (b) What is the car s speed at this level, again ignoring friction? (c) If the car s speed after ascending the hill is actually 10.1 m s, how much energy has been lost from the start because of the friction between the track and the coaster car? GPE plus KE at A are to converted to a new GPE plus a new KE at B. Compare this statement with the bar graphs of frame For part (b) describe, in a single sentence, the energy conversion process as the roller coaster car moves from B to C. C B GPE plus KE at B are converted to a new GPE plus KE at C. Compare this statement to bar graphs (e) and (f) in frame

5 Energy - Unit 5.2B - Problem 5.2B A roller-coaster car of mass 480 kg is raised to an initial height of 18.0 m above ground level. With a speed of 1.3 m s the car begins its descent. (a) Ignoring friction, what is the car s speed when it reaches a horizontal section of track of height 4.0 m above ground level? The car ascends its first hill to reach a level of 8.5 m above ground. (b) What is the car s speed at this level, again ignoring friction? (c) If the car s speed after ascending the hill is actually 10.1 m s, how much energy has been lost from the start because of the friction between the track and the coaster car? In a single sentence, for part (c), describe the energy conversion process as the car moves from A to C. A C

6 5 138 Energy - Unit 5.2B - Problem 5.2B A roller-coaster car of mass 480 kg is raised to an initial height of 18.0 m above ground level. With a speed of 1.3 m s the car begins its descent. (a) Ignoring friction, what is the car s speed when it reaches a horizontal section of track of height 4.0 m above ground level? The car ascends its first hill to reach a level of 8.5 m above ground. (b) What is the car s speed at this level, again ignoring friction? (c) If the car s speed after ascending the hill is actually 10.1 m s, how much energy has been lost from the start because of the friction between the track and the coaster car? GPE plus KE at A are converted to HE, plus GPE plus KE at C. Compare this statement with the bar graphs of frame

7 Energy - Unit 5.2B - Problem 5.3B A small child of mass 18.2 kg (weight of 40 lb) jumps onto a mattress and compresses it by 10.3 cm. If the mattress compresses with an effective spring constant of 8574 N, (a) what is the m maximum height above the mattress to which the child is propelled? (b) What is the child s speed as it leaves the mattress? Describe in a single sentence the energy conversion process between the two important events in part (a) of the problem. (a) Spring at maxi mum compressi on (b) Spring uncompressed, bl ock at maxi mum h ei gh t Workbook for Introductory Mechanics Problem-Solving Copyright by Daniel M. Smith, Jr. Sponsored by FIPSE (U.S. Department of Education)

8 5 140 Energy - Unit 5.2B - Problem 5.3B A small child of mass 18.2 kg (weight of 40 lb) jumps onto a mattress and compresses it by 10.3 cm. If the mattress compresses with an effective spring constant of 8574 N, (a) what is the m maximum height above the mattress to which the child is propelled? (b) What is the child s speed as it leaves the mattress? The spring s EPE (compressed mattress) plus the child s GPE are converted to the child s new GPE. Compare this statement with the bar graphs in frame

9 Energy - Unit 5.2B - Problem 5.3B A small child of mass 18.2 kg (weight of 40 lb) jumps onto a mattress and compresses it by 10.3 cm. If the mattress compresses with an effective spring constant of 8574 N, (a) what is the m maximum height above the mattress to which the child is propelled? (b) What is the child s speed as it leaves the mattress? Write a statement of energy conversion for part (b) of the problem. (a) Spring at maxi mum compressi on (b) Spring uncompressed, bl ock i n moti on, just l eavi ng spri ng

10 5 142 Energy - Unit 5.2B - Problem 5.3B A small child of mass 18.2 kg (weight of 40 lb) jumps onto a mattress and compresses it by 10.3 cm. If the mattress compresses with an effective spring constant of 8574 N, (a) what is the m maximum height above the mattress to which the child is propelled? (b) What is the child s speed as it leaves the mattress? The spring s EPE plus the child s GPE are converted to the block s KE and new GPE. Compare this statement with the bar graphs in frame

11 Energy - Unit 5.2B - Problem 5.4B A child of mass 31.5 kg (weight of 69.3 lb) sits in a playground swing whose seat, 0.6 m above the ground, is supported by ropes of length 2.4 m. The child is given a push, and the swing rises to a maximum angle of 36 with the vertical. (a) What is the child s speed as the swing passes back through its rest position? (b) The child releases her grasp on the ropes as the swing moves forward at the bottom of its trajectory, and the child slides out of the swing. How far away from the release point does she land? Ignore air resistance Write a single sentence describing the energy conversion process in part (a) of the problem. 36 o A B Workbook for Introductory Mechanics Problem-Solving Copyright by Daniel M. Smith, Jr. Sponsored by FIPSE (U.S. Department of Education)

12 5 144 Energy - Unit 5.2B - Problem 5.4B A child of mass 31.5 kg (weight of 69.3 lb) sits in a playground swing whose seat, 0.6 m above the ground, is supported by ropes of length 2.4 m. The child is given a push, and the swing rises to a maximum angle of 36 with the vertical. (a) What is the child s speed as the swing passes back through its rest position? (b) The child releases her grasp on the ropes as the swing moves forward at the bottom of its trajectory, and the child slides out of the swing. How far away from the release point does she land? Ignore air resistance GPE at A is converted to KE at B. Compare this sentence with the bar graphs of frame

13 Energy - Unit 5.2B - Problem 5.5B A roller coaster car starts from rest on a track 21.3 m above the ground. It moves down an incline, then around a vertical loop. In the absence of friction, what is the speed of the car at the top of the loop, which is 15.4 m above the ground level? Describe, by writing a single sentence, the energy conversion between the two important events of the problem. A B (a) Workbook for Introductory Mechanics Problem-Solving Copyright by Daniel M. Smith, Jr. Sponsored by FIPSE (U.S. Department of Education)

14 5 146 Energy - Unit 5.2B - Problem 5.5B A roller coaster car starts from rest on a track 21.3 m above the ground. It moves down an incline, then around a vertical loop. In the absence of friction, what is the speed of the car at the top of the loop, which is 15.4 m above the ground level? The car s GPE at A is converted to a new GPE plus KE at B. Compare this statement with the bar graphs in frame 8.33.

15 Energy - Unit 5.2B - Problem 5.6B A playground slide has a straight inclined section which ends at the bottom in a short, horizontal section. The inclined section is 2.7 m in length and forms an angle of 40 with the horizontal. A 45 kg child moves down the whole length of the slide. (a) If she starts from rest, what is her speed at the bottom of the incline for a coefficient of kinetic friction of 0.12 between the child and the slide? (b) How much energy has been lost to heat when she reaches the incline s bottom? (c) What is the child s speed for the same heat energy loss if a curved section replaces the straight, inclined section? Write a single sentence describing the energy conversion between the two important events in part (a) of the problem. A B Workbook for Introductory Mechanics Problem-Solving Copyright by Daniel M. Smith, Jr. Sponsored by FIPSE (U.S. Department of Education)

16 5 148 Energy- Unit 5.2B - Problem 5.6B A playground slide has a straight inclined section which ends at the bottom in a short, horizontal section. The inclined section is 2.7 m in length and forms an angle of 40 with the horizontal. A 45 kg child moves down the whole length of the slide. (a) If she starts from rest, what is her speed at the bottom of the incline for a coefficient of kinetic friction of 0.12 between the child and the slide? (b) How much energy has been lost to heat when she reaches the incline s bottom? (c) What is the child s speed for the same heat energy loss if a curved section replaces the straight, inclined section? The child s GPE at A is converted to HE, plus KE at B. Compare this statement with the bar graphs of frame

17 Energy - Unit 5.2B - Problem 5.7B Starting from rest, a 1.7 kg block slides a distance of 2.1 m down a rough (µ k = 0.2), 20 incline before encountering a spring (k=23.5 N ). (a) What is the block s speed as it first touches the m spring? (b) By how much is the spring compressed? (c) How far back up the incline does the block move after it leaves the spring? Describe the energy conversion process in part (a) of the problem by writing a single sentence. A B Workbook for Introductory Mechanics Problem-Solving Copyright by Daniel M. Smith, Jr. Sponsored by FIPSE (U.S. Department of Education)

18 5 150 Energy - Unit 5.2B - Problem 5.7B Starting from rest, a 1.7 kg block slides a distance of 2.1 m down a rough (µ k = 0.2), 20 incline before encountering a spring (k=23.5 N ). (a) What is the block s speed as it first touches the m spring? (b) By how much is the spring compressed? (c) How far back up the incline does the block move after it leaves the spring? GPE at A is converted to HE, plus GPE plus KE at B. Compare this sentence with the bar graphs of frame

19 Energy - Unit 5.2B - Problem 5.7B Starting from rest, a 1.7 kg block slides a distance of 2.1 m down a rough (µ k = 0.2), 20 incline before encountering a spring (k=23.5 N ). (a) What is the block s speed as it first touches the m spring? (b) By how much is the spring compressed? (c) How far back up the incline does the block move after it leaves the spring? Write a sentence of energy conversion between the two important events for part (b) of the problem. B C (a) (b)

20 5 152 Energy - Unit 5.2B - Problem 5.7B Starting from rest, a 1.7 kg block slides a distance of 2.1 m down a rough (µ k = 0.2), 20 incline before encountering a spring (k=23.5 N ). (a) What is the block s speed as it first touches the m spring? (b) By how much is the spring compressed? (c) How far back up the incline does the block move after it leaves the spring? KE plus GPE at B are converted to HE, plus EPE plus GPE at C. Compare this statement with the bar graphs of frame

21 Energy - Unit 5.2B - Problem 5.7B Starting from rest, a 1.7 kg block slides a distance of 2.1 m down a rough (µ k = 0.2), 20 incline before encountering a spring (k=23.5 N ). (a) What is the block s speed as it first touches the m spring? (b) By how much is the spring compressed? (c) How far back up the incline does the block move after it leaves the spring? Describe, in a single sentence, the energy conversion for part (c) of the problem. D C (a) (b)

22 5 154 Energy - Unit 5.2B - Problem 5.7B Starting from rest, a 1.7 kg block slides a distance of 2.1 m down a rough (µ k = 0.2), 20 incline before encountering a spring (k=23.5 N ). (a) What is the block s speed as it first touches the m spring? (b) By how much is the spring compressed? (c) How far back up the incline does the block move after it leaves the spring? EPE plus GPE at C are converted to HE, plus GPE at D. Compare this statement with the bar graphs of frame