two rectangular cuboids on a hill · Physics Brawl 2022 #9
Physics · mechanics
Problem
Let us have "a hill" made of two inclined planes with inclinations α1 and α2 with respect to the horizontal plane. We lay a rectangular cuboid with the mass m1=10 kg on the first plane with inclination α1=25°. On the second plane with inclination α2=35°, we place a different rectangular cuboid with the mass m2=15 kg. Then we connect the cuboids with a massless rope that is led through a massless pulley at the top of the hill. The rope is always stretched parallel to the given plane, the coefficient of dynamic friction between the cuboids and inclined planes is f=0.15, and the coefficient of static friction is small enough for cuboids to start moving. What is the acceleration of the cuboid m1 if both cuboids are at rest at the beginning? The positive sign will indicate acceleration downhill, and a negative sign will indicate acceleration uphill.