Question

A horizontal spring with a spring constant of 190 N/cm is compressed 6.3 cm. A wooden block with a mass of 1.5 kg is placed in front of and in contact with the spring. When the spring is released it pushes the block, which slides on a frictionless horizontal surface for some distance. The block then slides up a frictionless incline of 27 degrees above the horizontal and comes to a momentary stop before sliding back down. The system is the spring, the block, the incline, and the Earth. Ignore air resistance.

A) What is the potential energy of the spring before it is released?

B) What is the kinetic energy and the speed of the block as it slides on the horizontal surface after the spring has pushed it?

C) At what height does the block stop on the incline?

D) If the incline were rough, how would the stopping height of the block compare to the stopping height when the incline is frictionless? Explain using energy.

Answer 1

A) What is the potential energy of the spring before it is released?

The elastic potential energy of the spring,

Convert N/cm to N/m and cm to m

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B) What is the kinetic energy and the speed of the block as it slides on the horizontal surface after the spring has pushed it?

When the spring is released, the elastic potential energy of the spring is converted to the kinetic energy of the block

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Kinetic energy,

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C) At what height does the block stop on the incline?

When the block climb the incline kinetic energy is converted to potential energy

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D) If the incline were rough, how would the stopping height of the block compare to the stopping height when the incline is frictionless? Explain using energy.

If the incline was rough when the block climb the incline, the kinetic energy is converted to potential energy but some portion of the kinetic energy will be lost to friction

In this case, the potential energy, will be less than

and final height climbed will be less than

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