Newton’s Second Law

Chapter 7. Newton’s Second Law

Newton’s Second Law

7-1. A 4-kg mass is acted on by a resultant force of (a) 4 N, (b) 8 N, and (c) 12 N. What are the resulting accelerations?

(a) 1 m/s2 (b) 2 m/s2 (c) 3 m/s2

7-2. A constant force of 20 N acts on a mass of (a) 2 kg, (b) 4 kg, and (c) 6 kg. What are the resulting accelerations?

(a) 10 m/s2 (b) 5 m/s2 (c) 3.33 m/s2

7-3. A constant force of 60 lb acts on each of three objects, producing accelerations of 4, 8, and 12 N. What are the masses?

15 slugs 7.5 slugs 5 slugs

7-4. What resultant force is necessary to give a 4-kg hammer an acceleration of 6 m/s2?

F = ma = (4 kg)(6 m/s2); F = 24 N

7-5. It is determined that a resultant force of 60 N will give a wagon an acceleration of 10 m/s2. What force is required to give the wagon an acceleration of only 2 m/s2?

; F = ma = (6 slugs)(2 m/s2); F = 12 N

7-6. A 1000-kg car moving north at 100 km/h brakes to a stop in 50 m. What are the magnitude and direction of the force? Convert to SI units: 100 km/h = 27.8 m/s

F = ma = (1000 kg)(7.72 m/s2); F = 772 N, South.

The Relationship Between Weight and Mass

7-7. What is the weight of a 4.8 kg mailbox? What is the mass of a 40-N tank?

W = (4.8 kg)(9.8 m/s2) = 47.0 N ; = 4.08 kg

7-8. What is the mass of a 60-lb child? What is the weight of a 7-slug man?

= 1.88 slugs ; W = (7 slugs)(32 ft/s2) = 224 lb

7-9. A woman weighs 180 lb on earth. When she walks on the moon, she weighs only 30 lb. What is the acceleration due to gravity on the moon and what is her mass on the moon? On the Earth?

Her mass is the same on the moon as it is on the earth, so we first find the constant mass:

mm = me = 5.62 slugs ;

Wm = mmgm ; gm = 5.33 ft/s2

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