A block of mass 5.00 kg rests at a height of 3.00 m from the horizontal plane. I

Question

A block of mass 5.00 kg rests at a height of 3.00 m from the horizontal plane. It is released and moves from point A to point B on a frictionless surface, continues to slide a distance of 6.00 m from B to C on a rough surface, then hits and compresses the spring on a frictionless surface before stopping momentarily. The force constant of the spring is 1500 N/m. What is the speed of the block just before point B?  If the friction force is 20.0 N, what is the speed of the block when it has passed point C? How much is the spring compressed when the block momentarily stops?

Explanation / Answer

speed of block just before point B, Vb= (2gh)= (2*9.81*3)= 7.7 m/s

acceleration from B to C, a = -friction force/mass= - 20/5= -4 m/s²

speed of block after passing point C, Vc

(Vc)² - (Vb)² = 2as

or, (Vc)² = 7.7² - 2*4*6

or, Vc= 3.36 m/s

Let the compression of spring be x

(1/2)kx²= (1/2)m(Vc)²

x² = 5*3.36²/1500

x= 0.194 m = 19.4 cm

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