Physics, 22.10.2020 19:01 josetheghost6313

The horizontal surface on which the block slides is frictionless. The speed of the block before it touches the spring is 6.0 m/s. How fast is the block moving at the instant the spring has been compressed 15 cm

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The final speed of the block moving at the instant the spring has been compressed is approximately 3.674 meters per second.

Explanation:

The spring constant is 2000 newtons per meter. Let consider the spring-block system, from Principle of Energy Conservation we can represent it by the following model:

$U_{k,1}+K_{1} = U_{k,2}+K_{2}$

$K_{2} = K_{1}+(U_{k,1}-U_{k,2})$ (Eq. 1)

Where:

$K_{1}$ , $K_{2}$ - Initial and final kinetic energies of the block, measured in joules.

$U_{k,1}$ , $U_{k,2}$ - Initial and final elastic potential energy, measured in joules.

And we expand the equation above by definitions of elastic potential energy and kinetic energy:

$\frac{1}{2}\cdot m \cdot v_{2}^{2} = \frac{1}{2}\cdot m\cdot v_{1}^{2} + \frac{1}{2}\cdot k\cdot (x_{1}^{2}-x_{2}^{2})$

$v_{2} = \sqrt{v_{1}^{2}+\frac{k}{m}\cdot (x_{1}^{2}-x_{2}^{2}) }$ (Eq. 1b)

Where:

- Mass of the block, measured in kilograms.

- Spring constant, measured in newtons per meter.

$v_{1}$ , $v_{2}$ - Initial and final velocities of the block, measured in meters per second.

$x_{1}$ , $x_{2}$ - Initial and final positions of spring, measured in meters.

If we know that $v_{1} = 6\,\frac{m}{s}$ , $k = 2000\,\frac{N}{m}$ , $m = 2\,kg$ , $x_{1} = 0\,m$ and $x_{2} = 0.15\,m$ , the final speed of the block moving at the instant the spring has been compressed is:

$v_{2} = \sqrt{\left(6\,\frac{m}{s} \right)^{2}+\left(\frac{2000\,\frac{N}{m} }{2\,kg} \right)\cdot [(0\,m)^{2}-(0.15\,m)^{2}]}$

$v_{2}\approx 3.674\,\frac{m}{s}$

The final speed of the block moving at the instant the spring has been compressed is approximately 3.674 meters per second.

The horizontal surface on which the block slides is frictionless. The speed of the block before it t

Answer from: Quest

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

Answer from: Quest

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