A 8 kg mass slides to the right on a surface having a coefficient of friction 0.24 as shown. The mass has a speed of 5 m/s when contact is made with a spring that has a spring constant 166 N/m. The mass comes to rest after the spring has been compressed a distance d. The mass is then forced toward the left by the spring and continues to move in that direction beyond the unstretched position. Finally the mass comes to rest a distance D to the left of the unstretched spring. v₁ = 0 8 kg 8 kg 5 m/s 8 kg v₂ = 0 166 N/m mmmmmmm D- kommy d 8 kg .vf Vf 8 kg m 166 N/m mmmmmm μ = 0.24 Find the compressed distance d. The accel- eration of gravity is 9.8 m/s². Answer in units of m.

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Find d 

A 8 kg mass slides to the right on a surface
having a coefficient of friction 0.24 as shown.
The mass has a speed of 5 m/s when contact is
made with a spring that has a spring constant
166 N/m. The mass comes to rest after the
spring has been compressed a distance d. The
mass is then forced toward the left by the
spring and continues to move in that direction
beyond the unstretched position. Finally the
mass comes to rest a distance D to the left of
the unstretched spring.
υ
v₁ = 0
8 kg
8 kg
5 m/s
8 kg m
v₂ = 0
166 N/m
mmmmmm
D-
8 kg mmmmm
8 kg m
mm
166 N/m
mmmmmmm
μ = 0.24
Find the compressed distance d. The accel-
eration of gravity is 9.8 m/s².
Answer in units of m.
Transcribed Image Text:A 8 kg mass slides to the right on a surface having a coefficient of friction 0.24 as shown. The mass has a speed of 5 m/s when contact is made with a spring that has a spring constant 166 N/m. The mass comes to rest after the spring has been compressed a distance d. The mass is then forced toward the left by the spring and continues to move in that direction beyond the unstretched position. Finally the mass comes to rest a distance D to the left of the unstretched spring. υ v₁ = 0 8 kg 8 kg 5 m/s 8 kg m v₂ = 0 166 N/m mmmmmm D- 8 kg mmmmm 8 kg m mm 166 N/m mmmmmmm μ = 0.24 Find the compressed distance d. The accel- eration of gravity is 9.8 m/s². Answer in units of m.
Expert Solution
Step 1

Law of conservation of energy:

According to this law, the total energy of a system remains constant.

 

Given that:

Mass                    m=8 kg

Spring constant  k=166 N/m

Initial speed         vi=5 m/s

Speed when the spring is compressed vc=0 m/s

Coefficient of friction   μ=0.24

Acceleration due to gravity g=9.8 m/s2

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