An air-track glider of mass 0.093 kg is attached to the end of a horizontal air

Question

An air-track glider of mass 0.093 kg is attached to the end of a horizontal air track by a spring with force constant 19.5 N/m

(a) With the air track turned off, the glider travels 8.1 cm before it stops instantaneously. How large would the coefficient of static friction s have to be to keep the glider from springing back to the left?

(b) If the coefficient of static friction between the glider and the track is s= 0.62, what is the maximum initial speed v1 that the glider can be given and remain at rest after it stops instantaneously? With the air track turned off, the coefficient of kinetic friction is k= 0.54.

0.6948 is the correct answer but I dont know how to get to it please explain and show the work :)

Explanation / Answer

here,

mass of the glider , m = 0.093 kg

spring constant , k = 19.5 N/m

(a)

distance travelled by the glider , x = 8.1 cm

x = 0.081 m

for the glider to do not move back

k * x = us * m * g

19.5 * 0.081 = us * 0.093 * 9.8

us = 1.73

the coefficient of static friction s have to be to keep the glider from springing back to the left is 1.73

(b)

us = 0.62

uk = 0.54

let the minimum initial speed be v0

let it travels x distance to stop instatanously

k * x = us * m * g

19.5 * x = 0.62 * 0.093 * 9.8

x = 0.029 m

using conservation of energy

0.5 * m * v0^2 = 0.5 * k * x^2 + uk * m * g * x

0.5 * 0.093 * v0^2 = 0.5 * 19.5 * 0.029^2 + 0.54 *0.093 * 9.8 * 0.029

v0 = 0.7 m/s

the maximum initial speed of the glider is 0.7 m/s

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