Physics- Springs and Swings

Question

A 3 kg block is pushed by an external force against a spring with spring constant 134 N/m until the spring is compressed by 2.1 m from its uncompressed length (x = 0). The block rests on a horizontal plane that has a coefficient of kinetic friction of 0.7 but is NOT attached to the spring.

After all the external forces are removed (so the compressed spring releases the mass) how far D along the plane will the block move before coming to a stop? The acceleration due to gravity is 9.8 m/s 2 . Answer in units of m.

Answer 1

Hello Chris! As I've told many other potential students, I won't really be ready to tutor until next year ( 2020 has been awful due to the pandemic ). I'll try to get the equations right from memory, and I'll check back later to see if my answer is correct.

If I remember correctly, the potential energy ( PE ) of a spring is 1/2 kx^2. If this is the case, an equivalent amount of work will be done on the box as it slides. The work ( W ) done will equal the force of friction over a distance ( Ff )( d ) = ( u )( N )( d ). Since the normal force ( N = mg ), work done on the block by friction is W = ( u )( mg )( d ).

Since ( Ff )( d ) = 1/2 kx^2, d = ( 0.5 kx^2 / ( u*mg ) = ( 0.5*134N/m*4.41m^2 / 20.58 N ) = 14.4 m.

Let me know if this is the answer you obtained.

Have a great day!