A block of mass m goes through the following motion. It is given a speed down a

Question

A block of mass m goes through the following motion. It is given a speed down a ramp of angle . There is friction between the block and the ramp and the coefficient of kinetic friction is µk. The block travels a distance L to a spring of force constant k and compresses the spring by a distance x before stopping.

e. Through the entire trip, what is the change in the kinetic energy of the block?

f. Through the entire trip, what is the change in the potential energy of the block?

g. Is mechanical energy conserved?

h. Solve for the initial speed needed to compress the spring by the distance x in terms of the variables given.

Explanation / Answer

e) change in kinetic energy= m*(Vx^2+Vy^2)/2

Where x=L*cos thetha

Vx=x dot

y=L*sin thetha

Vy=y dot

f)change in potential energy= (m*g*y)+(k*x^2)/2

Whereby=L* sin thetha

g) yes , mechanical energy is always conserved.

h) speed needed to compress the spring is equal to V^2=Vx^2+Vy^2

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