1. A 4.80kilogram hoop starts from rest at a height 1.40 m above the base of an inclined plane and rolls down under the influence of gravity. What is the linear speed of the hoop's center of mass just as the hoop leaves the incline and rolls onto a horizontal surface? (Neglect friction.) m/s 2. A uniform solid sphere rolls without slipping down a 23\" inclined plane. What is the acceleration of the spheres center of mass? The moment of inertia of a uniform solid sphere about an axis that passes through its center = %rnr2. The moment of inertia of a uniform solid sphere about an axis that is tangent to its surface : 7l5mr2. m/s2 3. A solid disk rotates in the horizontal plane at an angular velocity of 4.00 x 10'2 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.14 kg.m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk? rad/5 4. A L60 kg box rests on a plank that is inclined at an angle of 63.0D above the horizontal. The upper end of the box is attached to a spring with a force constant of 24.0 N/m, as shown in the gure. If the coefficient of static friction between the box and the plank is 0.23, what is the maximum amount the spring can be stigma and the box remain at rest? m 5. To measure the static friction coefcient between a 1.30-kg block and a vertical wall, a spring (k = 780 N/m) is attached to the block, is pushed on the end in a direction perpendicular to the wall until the block does not slip downward (see gure). If the spring is compressed by 0.048 m, what is the coefcient of static friction? 6. A spring that has a force constant of 1050 N/m is mounted vertically on the ground. A block of mass 1.40 kg is dropped from rest from height of 1.90 m above the free end of the spring. By what distance does the spring Compress? rn 7. When a 0.32kg block is suspended on a vertical spring, it causes it to stretch 2.90 cm. If the block is now pulled 8.40 cm below its equilibrium position and released, what is the speed of the block when it is 4.00 cm below the equilibrium position? m/s 8. Avertically mounted spring (k = 750 Mm) is compressed by 26.0 cm relative to its unstrained length. A mass (rn = 0.30 kg) is placed at rest against the spring. when the spring is released, the mass is launched vertically in the air. What is the speed of the mass (m) when it passes by a point located 5.75 m above the release point? m/s 9. A grandfather clock uses a pendulum that is 68.0 cm long. It is accidentally broken, and when repaired the length is shorter by 21.0 ETllTl. Treating the clock's pendulum as a simple pendulum, by how much will the repaired clock differ from the correct time every 24 hours