A block of mass 2 kg rests at a distance of 4 m from the edge of a rough horizontal table of height 5 m . The coefficient of kinetic friction between the block and the table is 0.2 . The block is struck by a horizontal hammer blow. The force of the blow is described by a triangular force-time ( F-t ) graph with a peak force of 2000 N and a base duration of 10 ms . After the blow, the block slides to the edge and fall

Step-by-step solution

The impulse J delivered to the block is the area under the F-t graph. J = 1 2 base height = 1 2 (10 10⁻³ s ) 2000 N = 10 N s Using the impulse-momentum theorem, the initial velocity v₀ of the block is: v₀ = J m = 10 2 = 5 m s ⁻¹ The block slides a distance d = 4 m on the rough table. The deceleration due to kinetic friction is: a = - _k g = -0.2 10 = -2 m s ⁻² Using the third equation of motion to find the velocity v at the edge of the table: v^2 = v₀^2 + 2ad v^2 = 5^2 + 2(-2)(4) = 25 - 16 = 9 v = 3 m s ⁻¹ Once the