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Musya8 [376]
3 years ago
14

Corey exerts a force of 35 N and moves a crate 3 m. How much work has he done on the crate?

Physics
1 answer:
Zinaida [17]3 years ago
6 0
105 J because work done is force times distance
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A 326 g object is attached to a spring and executes simple harmonic motion with a period of 0.250 s. If the total energy of the
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Answer:

a) v_{max}=5.98\frac{m}{s}

b) k=205.92\frac{N}{m}

c) A=0.24m

Explanation:

a) In the equilibrium position of the system, that is when the spring is not elongated, the potential energy is zero. Therefore, the total energy of the system is the maximum kinetic energy:

E=K_{max}\\E=\frac{mv_{max}^2}{2}\\v_{max}=\sqrt{\frac{2E}{m}}\\v_{max}=\sqrt{\frac{2(5.83J)}{0.326kg}}\\v_{max}=5.98\frac{m}{s}

b) The force constant of the spring can be calculated from the natural frequency of the system:

\omega^2=\frac{k}{m}\\k=m\omega^2

Recall that \omega=\frac{2\pi}{T}\\, that is the distance traveled in one revolution divided into the time of one revolution. Replacing and solving for k:

k=\frac{m4\pi^2}{T^2}\\k=\frac{(0.326kg)4\pi^2}{(0.25s)^2}\\k=205.92\frac{N}{m}

c) The maximum speed is directly proportional to the amplitude of the motion:

v_{max}=A\omega\\A=\frac{v_{max}}{\omega}\\A=\frac{(v_{max})T}{2\pi}\\A=\frac{(5.98\frac{m}{s})0.25s}{2\pi}\\A=0.24m

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