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  4. Chapter 3 The causes of motion: dynamics
  5. Chapter 3 Problems
  6. Answers to Chapter 3 problems

Answers to Chapter 3 problems

3.4.1 ; (a) 4.0 kg    (b) 8.0 kg    (c) 7 bricks

3.4.2 ; 7.9 m s−2 downwards

3.4.3  (a) 2.4 kg    (b) 24.0 N

3.4.4  8.87 × 103 N;   95 m

3.4.5  (a) 8.87 × 1014 N    (b) 5.1 × 106 m s−1

3.5.1 ; (a) 333 N    (b) 2.2 cm;   0.22 ms

3.5.2  61 m s−1

3.5.3  26 cm;   33 cm

3.6.1  8.0 s;   0.395 m;   − 0.219 m s−1;   0.172 m s−2

3.6.2  

3.6.3  0.54 s;   0.15 m;   0.10 m ;   1.28 m s−1

3.6.4  Period is \( { T_aT_b\over \sqrt{T_b^2+T_a^2}} \);   equilibrium position is \( { T_b^2a+T_a^2b \over {T_b^2+T_a^2}}. \)

3.6.5  (a) 4.0 s    (b) 0.63 m s−1

3.6.6  (a) 2.3 s    (b) 2.35 m s−2

3.6.7  3.7 s

3.6.8  (a) − 87 mm    (b) 0.69 m s−1    (c) − 1.5 m s−2

3.6.9  600 N m−1

3.6.10  

3.6.11  (a) \( { \sqrt{A_1^2+A_2^2}} \)     (b) \( {ω \sqrt{A_1^2+A_2^2}} \)     (c)  tan−1 \( {A_2 \over A_1} \) 

3.7.1  (a) \( {a \over 2x^2} - {b \over x} \)    (b) \( {a \over b} \)    (c) \( {2 Ï€ a \over b^2}\sqrt{ma} \) 

3.10.1 (a) x12 + x22 = A2    (b) ± 4.58 cm;   0.19    (c) 0.118 of the period.

3.10.2  (a) \( {2 Ï€ \over T}\sqrt{A^2-x^2} \)   (b) y =3; 2Ï€; 3

3.11.1  0.0135 kg s−1 ;   25.7 s

3.11.2  (a) − 14 mm    (b) 0.06 N (m s−1)−1;   3.5 N m−1    (c) 1.7 N (m s−1)−1

3.12.1  (a) 19.8 rad s−1    (b) 1.5 cm    (c) 86 mW

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