The acceleration of the 500g block in figure is xg/13, find x

Question

G1 Physics · Accepted Answer

Step 1: From the diagram: 500 g descends, pulling the 100 g block uphill, while a 50 g mass is connected on the opposite side. The incline is 30° and pulleys/strings are ideal. Step 2: Along the coupled motion, gravitational driving force is [0.500−0.050−0.100 sin30°]g = (0.500−0.050−0.050)g=0.400g. Step 3: Total moving mass =0.500+0.100+0.050=0.650 kg. Thus a=(0.400/0.650)g=(8/13)g. Step 4: The 500 g block has the same acceleration magnitude, so x=8. Answer: 8.