Question

Two crates with masses of 100 kg and 200 kg respectively are connected with a light inelastic rope. A force with magnitude F pulls the crates up an incline with an angle of 30° with the horizontal

The kinetic coefficient of friction for the 100 kg crate is 0,3 and that of the 200 kg crate is 0,5.

Calculate the Magnitude of F if the system moves at a constant velocity up the

incline.

Answer 1

for mass of 200 kg:

tension of rope:

$T=m_2gsin\alpha+F_{fr2}=m_2gsin\alpha+\mu_2m_2gcos\alpha$

$T=200g(sin30\degree+0.5cos30\degree)=1829$ N

for mass of 100 kg:

tension of rope:

$F=m_1gsin\alpha+F_{fr1}+T=m_1gsin\alpha+\mu_1m_1gcos\alpha+T$

$T=200g(sin30\degree+0.5cos30\degree)=1829$ N

$F=100g(sin30\degree+0.5cos30\degree)+1829=2743$ N