A block of wood is attached to a very lightweight metal rod, which is attached to a fixed pivot point on a table. The block is able to slide on the table with negligible friction, and the pivot is also free to rotate with negligible friction. The block's mass is M and the rod's length is {. A bullet is moving parallel to the table and perpendicular to the rod when it collides and embeds within the block. The bullet's speed just before entering the block is v and its mass is m. т (a) Find the angular momentum of the combined bullet-block system about the vertical pivot axis. (Use any variable or symbol stated above as necessary. Enter the magnitude.) (b) Find the fraction of the original kinetic energy of the bullet that is converted into internal energy within the bullet-block system during the collision. (Use any variable or symbol stated above as necessary.) AK K;

A thin rod of mass M and length is suspended vertically from a frictionless pivot at its upper end. A mass m of putty traveling horizontally with a speed v strikes the rod at its CM and sticks there. How high does the bottom of the rod swing? Express your answer in terms of the variables m, M, v, and appropriate constants. hbottom = ΜΕ ΑΣΦ ?

(Figure 1)A bob of mass mm is suspended from a fixed point with a massless string of length LL (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle θθ. How long does it take the bob to make one full revolution (one complete trip around the circle)? Express your answer in terms of some or all of the variables mm, LL, and θθ, as well as the free-fall acceleration gg.

Inclined plane diagram: Also String 1 String 2 String 1 B C A The diagram above shows Carts B and C which roll without friction over an inclined plane. The plane is inclined at an angle of theta = 0 away from vertical, as shown in the diagram. Carts B and C are connected by an essentially massless string. Another massless string runs from Cart B over a massless and frictionless pulley to a hanging block, Block A.

Consider a conical pendulum with a bob of mass m = 81.0 kg on a string of length L = 10.0 m that makes an angle of θ = 6.00° with the vertical. (Consider +î to be towards the center of the circular path and +ĵ to be upward.) A conical pendulum is shown. The string is of length L and a bob of mass m is attached to the end. The string makes an angle θ with the vertical. A dashed circle is present to show the horizontal circular path of the bob.   (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. N î +  N ĵ(b) Determine the radial acceleration of the bob. m/s2

Three beads are placed along a thin rod. The first bead, of mass m1 = 25 g, is placed a distance d1 = 0.75 cm from the left end of the rod. The second bead, of mass m2 = 11 g, is placed a distance d2 = 1.8 cm to the right of the first bead. The third bead, of mass m3 = 48 g, is placed a distance d3 = 3.9 cm to the right of the second bead. Assume an x-axis that points to the right. -Find the center of mass, in centimeters, relative to the left end of the rod.  (Xcm = ?)

A sphere of mass 1.0 kg and radius 0.21 m is suspended on the rod of length 0.49 m and mass 0.43 kg as it is shown in the figure. System can rotate around uppermost point. A bullet of mass 0.02 kg strikes the sphere as it shown in the figure (aiming directly to the center of the sphere) and embeds. Find minimum velocity of bullet which allows this system to just clear the top. The answer is 300.719752599215. Please show all steps on how to get to that answer.

Problem 1: A meter stick has mass m = .2 kg (distributed uniformly along its length) and a length of (of course) 1 meter. The stick is placed simultaneously on two weight scales: one at the 20 cm mark (with 0 cm at the far left end of the stick), the other at the 70 cm mark, with no other supports or weights. Remember that a weight scale supplies an upward force, equal to the reading on the scale. Calculate the reading on both scales. Call the reading on the left scale (at 20 cm) FL, and the reading on the right scale (at 70 cm) FR. 20 cm 70 cm

The mass M_1 slides on a 45 degree incline surface with a height of H, as shown in the figure . The mass is connected by a flexible rope, over a small pulley (its mass is neglected) and connected to another mass M_2 whose mass is equal to the previous block and is vertically hanging as shown below. The rope is long enough for two blocks to be at rest at height H/2 . The dimensions of the two blocks and the pulley are neglected compared to the height H, the blocks were left to move freely at time t=0 1- At time t> 0 find the vertical acceleration of the mass m_2 2- Which of the two blocks moves down? Calculate the time when it will hit the ground? 3- If the block stopped in the previous paragraph when it hit the ground, but the other block continued to move, clarify whether or not it will hit the pulley. Why?

Find the answer for the given: Let L be the length. Let M be the mass. A rod that has L and M was hunged from the one end of a frictionless pivot, and it was hanged vertically at rest (intially) A person fired one small ball of clay with mass (m) to the rod with a speed V(initial) and stuck to the end of the non pivoted area. Find the angle Of greatest rotation for the rod/clay system? M M,L V(initial)