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A horizontal spring with spring constant 100 N/m is
Chapter 11, Problem 47P(choose chapter or problem)
Problem 47P
A horizontal spring with spring constant 100 N/m is compressed 20 cm and used to launch a 2.5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Use work and energy to find how far the box slides across the rough surface before stopping.
Questions & Answers
QUESTION:
Problem 47P
A horizontal spring with spring constant 100 N/m is compressed 20 cm and used to launch a 2.5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Use work and energy to find how far the box slides across the rough surface before stopping.
ANSWER:
Step 1 of 2
We have to find how far the box slides across the rough surface before stopping.
The motion diagram for the box is as shown in the below figure.
The kinetic energy of the box with which it is launched is equal to the potential energy of the spring by law of conservation of energy.
\(K_{1}=\frac{1}{2} k(\Delta x)^{2}\)
Where,
\(k=100 \mathrm{~N} / \mathrm{m}\)
\(\Delta x=20 \mathrm{~cm}=0.2 \mathrm{~m}\)
Thus,
\(K_{1} =\frac{1}{2}(100)(0.2)^{2}\)
\(=2.0 \mathrm{~J}\)