An air-track glider of mass 0.099 kg is attached to the end of a horizontal air

Question

An air-track glider of mass 0.099 kg is attached to the end of a horizontal air track by a spring with force constant 24.5 N/m (a) With the air track turned off, the glider travels 8.5 cm before it stops instantaneously. How large would the coefficient of static friction us 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 ,-0.57, 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 A-052. m/s

Explanation / Answer

Since, there is no motion due equillibrium of horizontal forces

F = Fs

From Hooks law, F = Kx

and Normal Force, N = mg

friction force, Fk = N

mg = Kx

= (24.5 x 0.085)/(0.099 x 9.81)

= 2.15

b) Now, = 0.57

x' = (mg)/k

x' = (0.57 x 0.099 x 9.81)/(24.5)

x' = 0.023 m

so, from the law of conservation of energy

0.5 K x'2 = 0.5 mv2 - k mg x

0.5 x 24.5 x 0.0232 = 0.5 x 0.099 x v2 - (0.52 x 0.099 x 9.81 x 0.023)

v = 0.60 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.