Question

Which of the following tables gives information for the spring-mass system with the greatest total mechanical energy?

• A. $Mass=1.0kg,Frequency=5.0Hz,Maximumspeed=1.0m/s$
• B. $Mass=2.0kg,Frequency=20.0Hz,Maximumspeed=1.0m/s$
• C. $Mass=1.0kg,Frequency=20.0Hz,Maximumspeed=2.0m/s$
• D. $Mass=2.0kg,Frequency=1.0Hz,Maximumspeed=2.0m/s$
• E. $Mass=3.0kg,Frequency=2.0Hz,Maximumspeed=1.0m/s$

Answer 1

Answer: (D)

$Mass=2.0kg,Frequency=1.0Hz,Maximumspeed=2.0m/s$

Total mechanical energy of the system is equal to either maximum kinetic energy or maximum potential energy.

$\therefore$ Total energy $T.E=K.E_{max}=\frac{1}{2}m{v}_{max}^2$

(A) : $T.E_A=\frac{1}{2}\times 1.0\times (1.0{)}^2=0.5$ J

(B) : $T.E_B=\frac{1}{2}\times 2.0\times (1.0{)}^2=1.0$ J

(C) : $T.E_C=\frac{1}{2}\times 1.0\times (2.0{)}^2=2.0$ J

(D) : $T.E_D=\frac{1}{2}\times 2.0\times (2.0{)}^2=4.0$ J

(E) : $T.E_E=\frac{1}{2}\times 3.0\times (1.0{)}^2=1.5$ J

Hence option D is correct.