The three blocks shown are identical. Blocks B and C are at rest when block B is hit by block A, which is moving with a velocity $v_A$ of 3 ft/s. After the impact, which is assumed to be perfectly plastic (e = 0), the velocity of blocks A and B decreases due to friction, while block C picks up speed, until all three blocks are moving with the same velocity v. Knowing that the coefficient of kinetic friction between all surfaces is $\mu_{k}=0.20$ , determine (a) the time required for the three blocks to reach the same velocity, (b) the total distance traveled by each block during that time.

Let A and B be $n\times n$ matrices and O be the $n\times n$ zero matrix. Use block multiplication to compute $$ \begin{equation*}\begin{bmatrix}A&&B\\text{\O}&&O\end{bmatrix}^k\end{equation*} $$ for any positive integer k.

The system consists of a light, inextensible cord, light, frictionless pulleys, and blocks of equal mass. Notice that block B is attached to one of the pulleys. The system is initially held at rest so that the blocks are at the same height above the ground. The blocks are then released. Find the speed of block A at the moment the vertical separation of the blocks is h.

A 4-kg block rests on top of a 5-kg block, which rests on a frictionless table. The coefficient of friction between the two blocks is such that the blocks start to slip when the horizontal force F applied to the lower block is 27 N. Suppose that a horizontal force is now applied only to the upper block. What is its maximum value for the blocks to slide without slipping relative to each other?

The 50-kg block rests on the horizontal surface, and a force P = 200 N, whose direction can be varied, is applied to the block. (a) If the block begins to slip when $\theta$ is reduced to $30^{\circ}$, calculate the coefficient of static friction $\mu_s$ between the block and the surface. (b) If P is applied with $\theta$ = $45^{\circ}$, calculate the friction force F.

A 6.0-kg block rests on top of a 7.0-kg block, which rests on a horizontal table.