A 1.10 kg mass slides to the right on a surface having a coefficient of kinetic

Question

A 1.10 kg mass slides to the right on a surface having a coefficient of kinetic friction 0.250. The object has a speed of vi = 3.20 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring.

(a) Find the distance of compression d.
??    m

(b) Find the speed v at the unstretched position when the object is moving to the left.
?? m/s

(c) Find the distance D where the object comes to rest.
?? m

Explanation / Answer

a) Here initial KE is converted into frictional energy and spring PE

KEi= Ef+SPE

1/2mv^2=uk*mg*x+1/2kx^2

½*1.1*3.2^2 = 0.25*1.1*9.8*d+1/2*50*d^2        => d= 0.42m

b) Spring PE is converted into KE

1/2kx^2 = 1/2mv^2

v= sqrt(k/m)*x =sqrt(0.25/1.1)*0.42 = 0.20m/s

c) Here KE is converted into frictional energy

1/2mv^2= uk*mg*D

½*1.1*0.20^2 = 0.25*1.1*D                =>    D= 0.08m= 8cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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