How much work would it take to horizontally accelerate an object with a mass of #8 kg# to #3 m/s# on a surface with a kinetic friction coefficient of #1 #?
1 Answer
Explanation:
Concept 1
In the problem, it is important to note that there is no friction. In the formula,
#F_f=muF_N#
Concept 2
To solve the problem, you must use two formulas:
#color(blue)(|bar(ul(color(white)(a/a)W=DeltaE_kcolor(white)(a/a)|)))#
where:
#W=# work (joules)
#DeltaE_k=# change in kinetic energy (joules)
#color(blue)(|bar(ul(color(white)(a/a)E_k=1/2mv^2color(white)(a/a)|)))#
where:
#m=# mass (metres)
#v=# velocity (metres per second)
Solving for Work
Start by breaking down
#W=DeltaE_k#
#W=E_(k,"final")-E_(k,"initial")#
#W=1/2mv_f^2-1/2mv_i^2#
#W=1/2m(v_f-v_i)^2#
Substitute your values.
#W=1/2(8kg)(3m/s-0m/s)^2#
Solve.
#W=1/2(8kg)(3m/s)^2#
#W=color(green)(|bar(ul(color(white)(a/a)color(black)(36J)color(white)(a/a)|)))#