UNIT HOMEWORK MOMENTUM ANSWER KEY

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1 UNIT HOMEWORK MOMENTUM ANSWER KEY MOMENTUM FORMULA & STUFF FROM THE PAST: p = v, TKE = ½v 2, d = v t 1. An ostrich with a ass of 146 kg is running to the right with a velocity of 17 /s. a. Calculate the oentu (in kg /s) of the ostrich. p = v = 146 kg 17 /s = 2482 kg /s b. Calculate the kinetic energy (in J) of the ostrich. TKE = ½ v 2 = ½ (146 kg)(17 /s) 2 = 21,097 J c. Calculate the distance (in ) travelled by the ostrich after 5 seconds. d = v t = 17 /s 5 s = A 21 kg child is riding a 5.9 kg bike with a velocity of 4.5 /s to the left. a. Calculate the oentu (in kg /s) of the child-bike syste. p = v = (21 kg kg) 4.5 /s = (26.9 kg) 4.5 /s = kg /s b. Calculate the kinetic energy (in J) of the child-bike syste. TKE = ½ v 2 = ½ (26.9 kg)( 4.5 /s) 2 = J c. Calculate the distance (in ) travelled by the child-bike syste after 5 seconds. d = v t = 4.5 /s 5 s = 22.5 COLLISIONS: ELASTIC 3. The ostrich fro Probl. 1 collides with the child and his bike fro Probl. 2. Assue the collision is elastic. Make the right the positive direction. a) What is the total oentu of the ostrich/child/bike syste together (in kg /s)? ptotal = postrich + pchild/bike = 2482 kg /s kg /s = kg /s b) What is the total kinetic energy of the ostrich/child/bike syste together (in J)? TKEtotal = TKEostrich + TKEchild/bike = 21,097 J J = 21,369.4 J c) If the child-bike syste bounces back with a velocity of 3 /s, what is the final velocity of the ostrich (in /s)? v1 + 2v2 = v3 + 2v4 2v4 v1 + 2v2 2v4 = v3 1 v v 2 2 v 4 1 (146 kg)(17 s ) + (26. 9 kg)( 4. 5 s ) (26. 9 kg)(3 s ) 146 kg kg 2v /s d) How uch kinetic energy (in J) does the child/bike syste have after the collision? TKE = ½ v 2 = ½ (26.9 kg)( 3 /s) 2 = J e) How uch kinetic energy (in J) does the ostrich have? TKE = ½ v 2 = ½ (146 kg)(15.62 /s) 2 = 17, J f) Was kinetic energy conserved? YES NO TKEfinal TKEinitial. looks like the collision was not copletely elastic.17, J 21,369.4 J g) Was oentu conserved? YES NO kg /s = kg /s

2 COLLISIONS: INELASTIC 4. The ostrich fro Probl. 1 collides with the child and his bike fro Probl. 2. Assue the collision is inelastic. a) What is the total oentu (in kg /s) of the ostrich/child/bike syste together? Nothing has changed. ptotal = postrich + pchild/bike = 2482 kg /s kg /s = kg /s b) What is the ass (in kg) of the ostrich/child/bike syste together? 146 kg kg = kg c) What is the final velocity (in /s) of the ostrich/child/bike syste together? v1 + 2v2 = ( + 2)v3 v1 + 2v2 = ( + 2)v3 ( + 2) ( + 2) 1 v v (146 kg)(17 s )+(26.9 kg)( 4.5 s ) (146 kg kg) kg /s d) Will the syste be oving to the right or to the left? The syste will be oving in the positive direction which in this case is to the right. e) How uch kinetic energy (in J) does the ostrich/child/bike syste have? TKE = ½v 2 = ½(172.9 kg)(13.66 /s) 2 = J f) Was kinetic energy conserved? YES NO TKEfinal TKEinitial. While total energy is conserved, soe of the echanical energy (kinetic) converted into work/heat. g) Was oentu conserved? YES NO Yes. pfinal = pinitial kg /s = kg /s IMPULSE/MOMENTUM: Ipulse = F t, p = v, d = v t 5. A 0.50 kg football is thrown with a velocity of 15 /s. A stationary receiver catches the ball and brings it to rest in s. What is the force (in N) exerted on the receiver? F t = v v F = t F = (0.50 kg) (15 s ) s = 375 N

3 6. A 0.50 kg object is at rest. A 3.00 N force acts on the object during a tie interval of 1.50 s. The force acts toward the right. a) What is the velocity (in /s) of the object at the end of this interval? F t = v F t = v 3.0 N (1.50 s) 0.50 kg = v 9 /s = v b) At the end of this interval, a constant fore of 4.00 N to the left is applied for 3.00 s. What is the velocity (in /s) at the end of the 3.00 s? The force is to the left so it is negative. We need to realize v = v f v i and that we have an initial velocity, vi, of 9 /s fro the previous proble. F t = v F t 4.0 N (3.00 s) 0.50 kg F t F t +v i = v = v f v i + v i + v i = v f + 9 s = v 15 /s = v 7. A 2.5 kg eteorite traveling at 30 /s landed in Mario s front yard. It ade a 0.5 hole in the ground. What force (in N) did it take to stop the eteorite? Ein = Eout TKEin = Wout ½v 2 = Fout dout ½v 2 d out ½(2.5 kg)(30 s )2 (0.5 ) = F out = F out 2250 N = Fout

4 COLLISIONS TWO DIMENSIONS: p = v 8. A 2 kg object is at rest. A 4 kg object collides against it with a velocity of 5 /s sending it flying off at an angle of 30 to the horizontal with a velocity of 8 /s. What is the final velocity of the 4 kg object, if it oves off at an angle of 65? pin = pout v1 = va cos a + 2 vb cos b 2 vb cos b 2 vb cos b v1 2 vb cos b v1 2 vb cos b = va cos a 1 v 1 2 v b cos b = v 1 cos a a (4 kg)(5 s ) (2 kg)(8 ) cos (30 ) s = v 4 kg cos (65 ) a 3.63 /s = v a 9. A 0.25 kg cue ball strikes the eight ball (0.30 kg) elastically and the cue ball oves off at an angle of 45 to the horizontal at 3 /s while the eight ball oves off at an angle of +60 to the horizontal at a velocity of 5 /s. What is the initial velocity (in /s) of the cue ball? pin = pout v1 = va cos a + 2 vb cos b v1 = va cos a + 2 vb cos b v 1 = 1 v a cos a + 2 v b cos b 1 BEFORE 4 kg 2 kg 5 /s AFTER BEFORE 2 kg = 30 = kg 0.30 kg? /s AFTER 0.30 kg 4 kg = 60 = kg (0.25 kg) (3 v 1 = s ) cos (45 ) + (0.30 kg)(5 s ) cos (60 ) 0.25 kg v1 = 5.12 /s

5 MOMENTUM: CONCEPTUAL QUESTIONS (c) 1. A oderate force will break an egg. However, an egg dropped on the road usually breaks, while one dropped on the grass usually does not break because for the egg dropped on the grass, a) the change in oentu is less. b) the change in oentu is greater. c) the tie interval for stopping is less. d) The tie interval for stopping is greater. The two eggs have the sae ass and velocity right before they strike the ground, so their oentus are equal. p egg1 = p egg2 p = v = F t The change of oentu ( p) equals the ipulse (F t) Which of the two eggs experience the greater force. Well, if the left hand side is the sae for both eggs (because they have equal ass and velocity as we entioned before) p egg1 = p egg2 = v and the tie of ipact (t) would be ore for the egg dropped on the grass, then v = F t the force of ipact ust be sall because the tie of ipact is great. (a) 2. A child falls sideways off a sled while sledding on frictionless ice. What happens to the velocity of the sled? a) It increases. b) It reains the sae. c) It decreases. d) cannot be deterined fro the inforation given The velocity increases. In order to fall off, the child ust apply a force to the sled over a period of tie. S/he gives ipulse (F t) to the sled. This ipulse equals the change in oentu of the sled, p = v. The ass of the sled/child syste decreased since the child fell off so, the velocity ust increase. (a) 3. Which of the following stateents properly relates the variables in the equation F t = p? a) A large constant force acting over a long tie interval causes a large change in oentu. b) A large constant force acting over a short tie interval causes a large change in oentu. c) Force and tie are directly proportional. The bigger the force, the longer the tie. d) Force and oentu are inversely proportional. The larger the force, the saller the change in oentu. In the relationship F t = p, oentu ( p) is proportional to force (F) and tie ( t), so the bigger either quantity gets, the bigger the change in oentu gets. (a) 4. Two objects stick together and ove with sae velocity after colliding. Identify the type of collisions. a) perfectly inelastic b) perfectly elastic c) partially inelastic d) partially elastic This is a perfectly inelastic collision, when the objects stick together as if they were one object. (b) 5. The law of conservation of oentu states that a) the total oentu of all objects interacting with one another is zero. b) the total oentu of all objects interacting with one another reains constant regardless of the nature of the forces between the objects. c) The total initial oentu of all objects interacting with one another does not equal the total final oentu. d) The total initial oentu of all objects interacting with one another usually equals the total final oentu. The forces that interfere with the law of conservation of oentu are external forces, not internal ones between the objects. (d) 6. An ice skater initially skating at a velocity of 3 /s speeds up to a velocity of 5 /s. The oentu of the skater a) becoes zero. b) decreases. c) reains the sae. d) increases. increases. The ass of the skater does not change so if his velocity increases, so does his oentu. p = v.

6 (d) 7. Two skaters stand facing each other. One skater s ass is 60 kg and the other s ass is 72 kg. If the skaters push away fro each other without spinning, a) the 60 kg skater travels with a lower oentu. b) their total oentu decreases. c) their total oentu doubles. d) their total oenta are equal but opposite. the aount of force with which each skater pushes off each other is the sae and the aount of tie of contact between the two skaters is the sae. They have the sae ipulse, J = F t, so they have the sae oentu, p = v, because F t = v (b) 8. A golf ball traveling 3.0 /s to the right collides in a head-on collision with a stationary bowling ball in a friction-free environent. If the collision is alost perfectly elastic, the speed of the golf ball iediately after the collision is a) slightly less than 3.0 /s. b) slightly greater than 3.0 /s. c) equal to 3.0 /s. d) uch less than 3.0 /s. The speed would be greater because the golf ball s ass is less than that of the bowling ball. (d) 9. Tightrope walkers walk with a long flexible rod in order to a) increase their total weight. b) allow both hands to hold onto soething. c) ove faster along the rope. d) lower their center of ass. The lowered center of ass akes the tightrope walker ore stable and less prone to start spinning/teetering on the rope. (a) 10. A rubber ball with a speed of 5.0 /s collides head-on elastically with an identical ball at rest. What is the speed of the initially stopped ball after the collision? a) zero c) 2.5 /s b) 1.0 /s d) 5.0 /s This is a Newton s Cradle proble. The incident ball will coe to a coplete stop and the other ball will bounce away with precisely the sae velocity as the incident ball. (c) 11. A 3.0-kg object oves to the right at 4.0 /s. It collides head-on with a 6.0-kg object oving to the left at 2.0 /s. Which stateent is correct? a) The total oentu both before and after the collision is 24 kg /s. b) The total oentu before the collision is 24 kg /s, and after the collision is 0 kg /s. c) The total oentu both before and after the collision is zero. d) None of the above is true. The oentu of the 3.0 kg object is p = v = 3 kg 4 /s = 12 kg /s The oentu of the 6.0 kg object is p = v = 6 kg 2 /s = 12 kg /s The total oentu is 12 kg /s 12 kg /s = 0 (b) 12. Two equal ass balls (one red and the other blue) are dropped fro the sae height, and rebound off the floor. The red ball rebounds to a higher position. Which ball is subjected to the greater agnitude of ipulse during its collision with the floor? a) It's ipossible to tell since the tie intervals and forces are unknown. b) Both balls were subjected to the sae agnitude ipulse. c) the blue ball d) the red ball Both balls have the sae ass and the sae velocity right before hitting the ground so they have the sae oentu and since ipulse = oentu (J = p F t = v), they have the sae ipulse. What is different is that the red ball experiences a larger Force (F in Newtons) so it ust be in contact with the ground for less tie t (in s). That is why it rebounds higher (it is ore elastic). (a) 13. A rubber ball and a lup of putty have equal ass. They are thrown with equal speed against a wall. The ball bounces back with nearly the sae speed with which it hit. The putty sticks to the wall. Which objects experiences the greater oentu change? a) the ball c) Both experience the sae oentu change. b) the putty d) cannot be deterined fro the inforation given The ball has a oentu of p = v as it hits the wall. It rebounds with a oentu p = ( v). The change in oentu is p = p f p i = v v = 2 v. In the case of the putty, the final velocity is zero so: p = p f p i = (0) v = v. The change in oentu of the elastic ball is twice that of the putty.