Question

A box is sliding down an incline tilted at a 16.0 angle above horizontal. The box is initially sliding down the incline at a speed of 1.90 m/s. The coefficient of kinetic friction between the box and the incline is 0.420. How far does the box slide down the incline before coming to rest?

A) 2.33 m

B) 0.720 m

C) 1.78 m

D) 1.44 m

E) The box does not stop. It accelerates down the plane

Answer 1

d) 1.44m

Step-by-step explanation:

According to Newton's second law:

`\sum F=m.a\\`

analyzing the horizontal components of the force:

`\sum F_x=mg*sin(\theta)-\µ*m.g*cos(\theta)\\\sum F_x=m*9.8*(sin(16^o)-0.420*cos(16^o))\\\sum F_x=-1.25m`

applying the second law

`-1.25m=m.a\\a=-1.25m/s^2`

given the acceleration we can calculate the distances traveled before stopping:

`(v_f)^2=(v_o)^2+2.a.\Delta x\\0=(1.90m/s)^2-2(1.25)*\Delta x\\\Delta x=1.44m`