Physics Forces Question

Question

An inclined surface, at angle θ=θ=15.1∘∘ with the horizontal, is constructed on a lab bench. A box, with mass m1=m1=3.02kgkg, is placed on the inclined surface, and it is attached to an ideal, meaning massless and inelastic, string that passes over an ideal, meaning massless and frictionless, pulley. The other end of the string is attached to a ball of mass m2=m2=0.298kgkg. The box is given an initial velocity with magnitude v=v=2.49m/sm/s directed parallel to and up the inclined surface, as shown in the drawing. The coefficient of kinetic friction is 0.29.

a.) What is the distance, in meters, that the box travels up the inclined surface before coming to rest?

b.) What is the minimum value of the coefficient of static friction such that, after coming to a stop, the box remains at rest and does not accelerate down the inclined box?

Answer 1

Answer 2

Thank you for submitting such a fun question! While the question is titled "Physics Forces Question", I find that the best way to go about solving this is using Energy Conservation.

My final answer is in the form of a formula containing all of the given variables, but if you wish to find r as a number value, simply plug in all of the given quantities in a calculator!

Also quick note: I am aware that I did omit the forces of tension acting on the masses in my force diagram; because we are solving using energy, this does not affect our final answer :)

Happy physic-ing!