How much work would it take to horizontally accelerate an object with a mass of #6 kg# to #7 m/s# on a surface with a kinetic friction coefficient of #1 #?

Question

How much work would it take to horizontally accelerate an object with a mass of #6  kg# to #7 m/s# on a surface with a kinetic friction coefficient of #1  #?

William Audy · Accepted Answer

#147J#

Concept 1 In the problem, it is important to note that there is no friction. In the formula,

#F_f=muF_N#

#mu# represents the constant of proportionality. But since it equals to #1#, #F_f=F_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 #DeltaE_k# into final kinetic energy minus the initial kinetic energy.

#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(6kg)(7m/s-0m/s)^2#

Solve.

#W=1/2(6kg)(49m^2/s^2)#

#W=color(green)(|bar(ul(color(white)(a/a)color(black)(147J)color(white)(a/a)|)))#

Lily Adams · Answer

undefined The work done to horizontally accelerate an object can be calculated using the formula:

Work = Force × Distance

The force required to overcome friction and accelerate the object can be calculated using Newton's second law:

Force = Mass × Acceleration

The acceleration can be determined using the equation of motion:

Final velocity^2 = Initial velocity^2 + 2 × Acceleration × Distance

Given:
- Mass (m) = 6 kg
- Final velocity (v_f) = 7 m/s
- Initial velocity (v_i) = 0 m/s
- Friction coefficient (μ) = 1

Acceleration can be found from the equation of motion:

7^2 = 0 + 2 × a × d
49 = 2ad
a = 49 / (2d)

Now, using Newton's second law:

Force = m × a

And the work done is given by:

Work = Force × Distance

Substituting the values, the work done can be calculated.