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Lesson Print NAME ______________________________________
DATE _______________ CLASS ____________________
Holt Physics
Problem 6B FORCE AND MOMENTUM PROBLEM
A student with a mass of 55 kg rides a bicycle with a mass of 11 kg. A net force of 125 N to the east accelerates the bicycle and student during a time interval of 3.0 s. What is the final velocity of the bicycle and student? Assume the student and bicycle are initially at rest. SOLUTION
Given:
ms = 55 kg mb = 11 kg F = 125 N to the east ∆t = 3.0 s vi = 0 m/s
Unknown:
vf = ?
Use the impulse-momentum theorem to solve for vf. F∆t = ∆p = mvf − mvi F∆t + mv vf = i m m = ms + mb = 55 kg + 11 kg = 66 kg (125 N)(3.0 s) − (66 kg)(0 m/s) vf = 66 kg
(125 N)(3.0 s) vf = 66 kg vf = 5.7 m/s to the east
ADDITIONAL PRACTICE 1. A net force of 10.0 N to the right pushes a 3.0 kg book across a table. If the force acts on the book for 5.0 s, what is the book’s final velocity? Assume the book to be initially at rest. 2. A 60.0 g egg dropped from a window is caught by a student. If the student exerts a net force of −1.5 N over a period of 0.25 s to bring the egg to a stop, what is the egg’s initial speed? 3. A child riding a sled is pulled down a snowy hill by a force of 75 N. If the child and sled have a combined mass of 55 kg, what is their speed after 7.5 s? Assume the child and sled are initially at rest. 4. A billiard ball with a mass of 0.195 kg and a velocity of 0.850 m/s to the right is deflected by the cushioned edge of the billiard table. The cushion exerts a force of 3.50 N to the left for 0.0750 s. What is the ball’s final velocity? Problem 6B
Ch. 6-3
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DATE _______________ CLASS ____________________
5. A 5.00 g projectile has a velocity of 255 m/s to the right. What force is required to stop this projectile in 1.45 s? 6. The Pacific walrus has an average mass of 1.1 × 103 kg and can swim with a speed of about 9.7 m/s. Suppose a walrus starting from rest takes 19 s to reach a velocity of 9.7 m/s to the east. What net force acts upon the walrus? 7. With a mass of 3.000 × 103 kg, the Russian-made Zil-41047 is the most massive automobile to have been manufactured on a regular basis. Suppose one of these cars accelerates from rest to a velocity of 8.9 m/s to the right in 5.5 s. Calculate the net force acting on the Zil-41047. 8. How much time would it take for a 0.17 kg ice hockey puck to decrease its speed by 9.0 m/s if the coefficient of kinetic friction between the ice and the puck is 0.050? 9. A girl pulls a 12.0 kg wagon along by exerting a force of 15.0 N on the wagon’s handle, which makes an angle of 20.0° with the horizontal. Friction provides a force of 11.0 N in the opposite direction. How long does it take for the wagon, which is initially at rest, to reach a speed of 4.50 m/s?
10. The compressed-air device at Sandia Laboratories in Albuquerque, New Mexico, accelerates small metal disks to a speed of 15.8 km/s. Suppose the compressed air exerts a force of 12.0 N on a 0.20 g disk that is initially at rest. How long will it take the disk to reach its maximum speed?
Ch. 6-4
Holt Physics Problem Bank
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Solutions
8. v = 50.0 km/h p = 0.278 kg•m/s
0.278 kg•m/s p m = = v (50.0 km/h)(103 m/km)(1 h/3600 s) m = 2.00 × 10−2 kg = 20.0 g
9. vavg = 96 km/h to the southeast pavg = 4.8 × 104 kg•m/s to the southeast 10. v = 255 km/s 36
p = 8.62 × 10 kg•m/s
4.8 × 104 kg•m/s p p vg = m = = a (96 km/h)(103 m/km)(1 h/3600 s) v vavg m = 1.8 × 103 kg
p 8.62 × 1036 kg•m/s m = = = 3.38 × 1031 kg v 255 × 103 m/s
Additional Practice 6B ∆p = mvf − mvi = F∆t
∆t = 5.0 s
(10.0 N)(5.05) + (3.0 kg)(0 m/s) F∆t + mv vf = i = = 17 m/s 3.0 kg m
vi = 0 m/s
vf = 17 m/s to the right
m = 3.0 kg
2. m = 60.0 g F = −1.5 N
∆p = mvf − mvi = F∆t
∆t = 0.25 s
mvf − F∆t (60.0 × 10−3 kg)(0 m/s) − (−1.5 N)(0.25 s) (1.5 N)(0.25 s) vi = = = −3 m 60.0 × 10−3 kg 60.0 × 10 kg
vf = 0 m/s
vi = 6.2 m/s
3. F = 75 N m = 55 kg
∆p = mvf − mvi = F∆t
∆t = 7.5 s
(75 N)(7.5 s) + (55 kg)(0 m/s) F∆t + mv vf = i = 55 kg m
vi = 0 m/s
vf = 1.0 × 101 m/s
4. m = 0.195 kg vi = 0.850 m/s to the right = +0.850 m/s F = 3.50 N to the left = −3.50 N ∆t = 0.0750 s
5. m = 5.00 g vi = 255 m/s to the right
∆p = mvf − mvi = F∆t (−3.50 N)(0.0750 s) + (0.195 kg)(0.850 m/s) F∆t + mv vf = i = 0.195 kg m −0.262 kg•m/s + 0.166 kg•m/s −0.096 kg•m/s vf = = = −0.49 m/s 0.195 kg 0.195 kg vf = 0.49 m/s to the left ∆p = mvf − mvi = F∆t
∆p mvf − mvi ∆t = = F F (0.20 × 10−3 kg)(15.8 × 103 m/s) − (0.20 × 10−3 kg)(0 m/s) ∆t = 12.0 N (0.20 × 10−3 kg)(15.8 × 103 m/s) ∆t = 12.0 N ∆t = 0.26 s
Additional Practice 6C 1. vi = 382 km/h to the right vf = 0 km/h mc = 705 kg md = 65 kg ∆t = 12.0 s
∆p (mc + md)vf − (mc + md)vi F = = ∆t ∆t [(705 kg + 65 kg)(0 km/h) − (705 kg + 65 kg)(382 km/h)](103 m//km)(1 h/3600 s) F = 12.0 s −(7.70 × 102 kg)(382 km/h)(103 m/km)(1 h/3600 s) F = = − 6.81 × 103 N 12.0 s F = 6.81 × 103 N to the left 1
V
1
∆x = 2(vi + vf)∆t = 2(382 km/h + 0 km/h)(103 m/km)(1 h/3600 s)(12.0 s) ∆x = 637 m to the right