Figure shows a block placed on a bracket. Bracket is placed on a smooth floor, it is pulled by a force F = 6N horizontally. Block is projected with velocity v₀ relative to bracket as shown in figure. Find time in second after which it stops relative to bracket. Horizontal surface of bracket is smooth while vertical surface is rough (Given: m = 1kg, M = 5kg, v₀ = 4m/s, μ = 0.5), the motion of bracket is restricted in z-direction.
Physics · Mixed Chapter
JEE Mains

Question

Figure shows a block placed on a bracket. Bracket is placed on a smooth floor, it is pulled by a force F = 6N horizontally. Block is projected with velocity v₀ relative to bracket as shown in figure. Find time in second after which it stops relative to bracket. Horizontal surface of bracket is smooth while vertical surface is rough (Given: m = 1kg, M = 5kg, v₀ = 4m/s, μ = 0.5), the motion of bracket is restricted in z-direction.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The block slides horizontally along the bracket's rough vertical wall in the y-direction shown; gravity does not decelerate this in-plane y motion. The bracket is on a smooth horizontal floor. Step 2: Total horizontal mass is M+m=5+1=6 kg. The external x-force is 6 N, so bracket and block share x-acceleration aₓ=F/(M+m)=1 m s⁻², maintained by a horizontal wall normal on the block N=maₓ=1 N. Step 3: Relative sliding is along horizontal y on the rough wall. Its friction magnitude is μN=0.…