Question

A machine pulls a 42 kg trunk 3.3 m up a 26o ramp at constant velocity, with the machine's force on the trunk directed parallel to the ramp. The coefficient of kinetic friction between the trunk and the ramp is 0.26. What are (a) the work done on the trunk by the machine's force and (b) the increase in thermal energy of the trunk and the ramp?

Answer 1

a) 911 J

b) 317 J

Step-by-step explanation:

because the acceleration is zero hence the truck is having a constant velocity, the net force on the truck is zero:

`\sum F=0\\F_m-F_g-F_f=0\\F_m=F_g+F_f\\\\F_g=m*g*sin(26^o)\\F_g=180N\\\\F_f=\µ*F_n\\F_f=0.26*42*9.8*cos(26^o)\\F_f=96N\\\\F_m=276N`

Because the force donde by the machine on the truck is paralle to the movement:

`W_m=F_m*d\\W_m=276*3.3\\W_M=911J`

The thermal energy is given by the work done by the friction:

`E_t=F_f*d\\E_t=96*3.3\\E_T=317J`