# Problem 2. The net external force acting on a block of M=3kg

Problem 2. The net external force acting on a block of M=3kg does a total of 54 J work on the block during the time interval from initial t(i)=0s, to final time t(f)=3s.(a) suppose that the initial speed of the particle is 0 ~v(o)=0m/s (i) use energetics to determine the final speed of the block (ii) ascertain the average net power input to block during the three second time interval. (b) Suppose that the initial speed of the particle is 8m/s (i) use energetics to determine the final speed of the block (ii) ascertain the instantaneous power input to the block at (A) beginning and (B) end of the three second interval(c) In another experiment, the same block was decelerated from an initial speed of 4m/s to an intermediate speed of 2m/s and then subsequently stopped. Ascertain the ratio of the amounts of work performed on the block to, first, halve it’s inital speed, and second, bring the block from the half-speed to rest.Problem 12. A block mass m=10kg is pushed along a frictional horizontal rail by an applied force with magnitude F(a), in such a way that it moves at a constant speed 3m/s, in the positive x-direction. The coefficient of kinetic friction acting between the block and the rail is u(k)=1/4. The initial position of the block is x(i)=om and its final position is x(f)=5m.(a) determine the force of kinetic friction acting on the block(b) Infer the magnitude and direction of the applied force acting on the block.(c) compute the mechanical work done by friction on the block as it moved from initial to its final position(d) compute the mechanical work done by the applied force acting on the block as it is displaced from its initial to its final(e) comment on the results obtain for (c) and (d)(f) compute the power input to the block by each of the forces individually(g) ascertain the net power input to the block. Comment.