Jason and Kim are attempting to push a heavy fridge across the kitchen floor. When Jason pushes it with a muscular force of 550. N, the fridge accelerates from rest to 28.0 cm/s in 3.50 s. When Kim pushes it with a muscular force of 560. N, the fridge accelerates from rest to 36.0 cm/s in 3.00 s. Calculate the coefficient of friction, and the mass of the fridge.

Question

Anonymous · Answer

v₁=0.280 m/s; t₁ =3.50 s; F₁=550 N
v₂=0.360 m/s; t₂=3.00s; F₂=560 N

ma₁ =F₁-F(fr) =F₁-μN =F₁- μmg
ma₂= F₂-F(fr)= F₂ -μN =F₂ - μmg

v₁= a₁t₁ => a₁=v₁/t₁ =>
ma₁ = m v₁/t₁=F₁ - μmg;
v₂= a₂t₂ => a₂=v₂/t₂ ->
ma₂ = m v₂/t₂=F₂ - μmg;

2m(v₂/t₂-v₁/t₁)= F₂-F₁-μmg + μmg
m=( F₂- F₁)/2(v₂/t₂-v₁/t₁)=
=(560-550)/2(0.360/3.00-0.280/3.50)=
=10/2(0.12-0.08)=125 kg;
μ=(F₁-mv₁/t₁)/mg =
(550 - 125•0.280/3.50)/125•9.8 =0.44