The spring shown in FIGURE is compressed 50 cm and used to

Chapter 11, Problem 57P

(choose chapter or problem)

QUESTION:

The spring shown in Figure P11.57 is compressed $50 cm$ and used to launch a $100 kg$ physics student. The track is frictionless until it starts up the incline. The student’s coefficient of kinetic friction on the $30^{\circ}$ incline is 0.15.

a. What is the student’s speed just after losing contact with the spring?

b. How far up the incline does the student go?

Questions & Answers

QUESTION:

a. What is the student’s speed just after losing contact with the spring?

b. How far up the incline does the student go?

ANSWER:

Step 1 of 2

Here we have to find the speed of the student, just after losing contact with the spring.

The mass of the student is,

$m=100\ kg$

The spring constant is,

$k=80000\ N/m$ .

The height is,

${y}_{0}={y}_{1}=10\ m$

${x}_{0}=0$

${v}_{0}=0$

${x}_{1}-{x}_{0}=0.5\ m$ .

The friction coefficient is,

${\mu{}}_{k}=0.15$ .

${v}_{2}=0$ .

Diagrammatically,

The conservation of energy demands,

${T}_{1}+{U}_{g1}{+U}_{s1}+\Delta{}{E}_{th}={T}_{o}+{U}_{g0}+{U}_{s0}+{W}_{ext}$

$\Rightarrow{}\frac{1}{2}m{{v}_{1}}^{2}+mg{y}_{1}+\frac{1}{2}k{\left({{x}_{1}-{x}_{2}}\right)}^{2}+0=\frac{1}{2}m{{v}_{0}}^{2}+mg{y}_{0}+\frac{1}{2}k{\left({{x}_{1}-{x}_{0}}\right)}^{2}+0$