×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

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 #3 #?

1 Answer
Jun 23, 2018

Answer:

The work is #=36J#

Explanation:

The mass is #m=8kg#

The acceleration due to gravity is #g=9.8ms^-2#

The coefficient of kinetic friction is #mu_k=3#

The normal force is #N=mg#

The force of friction is

#F_r=mu_kN=mu_kmg#

According to Newton's Second Law

#F=ma#

The acceleration is

#a=F/m=(mu_kmg)/m=mu_kg#

The speed is #v=3ms^-1#

The initial speed is #u=0ms^-1#

Apply the equation of motion

#v^2=u^2+2as#

The distance is

#s=v^2/(2a)=9/(2*mu_kg)=9/(2*3*9.8)=0.15m#

The work done is

#W=F*s=mu_kmg*s=3*8*9.8*0.15=36J#