Figure shows a system of cylinder (m = 50 kg) and a load (m = 30 kg) connected through a rope. The system is released from rest and the load L moves along the inclined surface. The kinetic coefficient of friction between the load and the inclined surface is 0.22. The radius of gyration of the cylinder is 0.8 m. Take d1 = 0.5 m, d2 = 1.4 m, and a = 34°. Determine the angular velocity of the cylinder after the load L slides 1.6 m on the inclined surface. d2 d1 C L

The circular bar shown in the figure is vertical.fixed by the support at point A in the plane. AThe spring constant connected to the support is k = 40 N/m. Broadcastingundeformed length, arc between circle ABis the distance. C fitting (bracelet) with a mass of 200 grams,connected to the spring and move in a frictionless circle bar.can. When the union is θ = 30° from the rest positionis being released. In this case, relative to point B of the fittingthe highest height it can reach and the highestcalculate the speed

3. A block of mass m = 2.00 kg rests on the left edge of a block of mass M = 8.00 kg. The coefficient of kinetic friction between the two blocks is 0.300, and the surface on which the 8.00 %3D kg block rests is frictionless. A constant horizontal force of magnitude F = 10.0 N is applied to the 2.00-kg block, setting it in motion as shown in Figure. The distance L that the leading edge of the smaller block travels on the larger block is 3.00 m. L M m M (a) Draw a separate free-body diagram for each block. (b) In what time interval will the smaller block make it to the right side of the 8.00-kg block? as (Note: Both blocks are set into motion when the force is applied.) (c) How far does the 8.00-kg block move in the process?

Figure shows a system of cylinder (m = 55 kg) and a load (m = 62 kg) connected through a rope. The system is released from rest and the load L moves along the inclined surface. The kinetic coefficient of friction between the load and the inclined surface is 0.22. The radius of gyration of the cylinder is 0.8 m. Take d1 = 0.5 m, d2 = 1.4 m, and a = 66°. Determine the angular velocity of the cylinder after the load L slides 1.6 m on the inclined surface. d2 d1 C The angular velocity of the cylinder is, [rad/s].

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The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration KG=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 0-0°. The spring's length at the state 2 is L2=4 m. (12) The kinetic energy at the state 2? (N-m) (two decimal places) LLLLKAL 2₂ तो State 2 Li State 1

In the figure, the hanging object has a mass of m1 = 0.420 kg; the sliding block has a mass of m2 = 0.850 kg, and the pulley is a hollow cylinder with a mass M = 0.350 kg, a interior radius R1 = 0.0200 m and an exterior radius R2 = 0.0300 m. Assume that the mass of the rays is negligible. The coefficient of kinetic friction between the block and the surface horizontal is µk = 0.250. The pulley rotates without friction on its axis. The lightweight cable does not stretch and does not slip on pulley. The block has a velocity of vi = 0.820 m / s towards the pulley when you pass a landmark on the table. (a) Use energetic methods to predict its velocity after it has passed a second point, which is at 0.700 m. (b) Find the angular speed of the pulley at the same moment.

The double pulley shown has a mass of 15 kg and a centroidal radius of gyration of 160 mm. Cylinder A and block B are attached to cords that are wrapped on the pulleys as shown in the figure. The coefficient of kinetic friction between block B and the surface is 0.2. Consider that the system is at rest in the position shown when a constant force P= 230 N is applied to cylinder A. 150 mm 250 mm 30° 15 kg 5 kg :1 m Determine the velocity of cylinder A as it strikes the ground. (You must provide an answer before moving on to the next part.) 5.5 * m/s The velocity of cylinder A as it strikes the ground is

Mass of both blocks = 14kg. The friction coefficient for this bar is µ= 0.4. The spring constant k= 60 N/m. The spring is compressed 0.1 m and then released. d a Find: www 1. The magnitude of block B's acceleration 2. The magnitude of tension of the rope A B a=?

The mechanism shown consists of a crank (bar AB), a connecting rod (bar BC) and the piston C that slides on the smooth surface (without friction). The combustion of gasoline produces a force P on the piston and this is kept in equilibrium with the moment M applied in A. The length of the crank is 116 mm, the length of the connecting rod is 183 mm, the force P is 710 N and the angle theta is 0.56 radians. Determine the value of M in Nm.