Gayle runs at a speed of 4.50 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After she has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m? Gayle's mass is 51.5 kg, the sled has a mass of 5.50 kg and her brother has a mass of 30.0 kg. m/s Need Help? Read ItA centrifuge in a medical laboratory rotates at an angular speed of 3,800 rev/min. When switched off, it rotates through 46.0 revolutions before coming to rest. Find the constant angular acceleration (in rad/s ) of the centrifuge. rad/s2 Need Help? Read It Watch ItA bicycle tire is spinning clockwise at 2.70 rad/s. During a time period At = 1.35 s, the tire is stopped and spun in the opposite (counterclockwise) direction, also at 2.70 rad/s. Calculate the change in the tire's angular velocity Aw and the tire's average angular acceleration day. (Indicate the direction with the signs of your answers.) HINT (a) the change in the tire's angular velocity Aw (in rad/s) |rad/s (b) the tire's average angular acceleration day (in rad/s2) rad/s2REMARKS Because the impact is inelastic, it would be incorrect to equate the initial kinetic energy of the incoming bullet to the nal gravitational potential energy associated with the bulletblock combination. The energy isn't conserved! QUESTION The ways that mechanical energy is lost from the system in this experiment include: [Select all that apply.) l: friction in the mechanisms l: energy loss from the change in height of the block l: thermal energy loss due to air drag l: friction to bring the bullet to a stop relative to the ground l: emission of sound waves PRACTICE IT Use the worked example above to help you solve this problem. The ballistic pendulum [Figure a] is a device used to measure the speed of a fast-moving projectile such as a bullet. The bullet is red into a large block of wood suspended from some light wires. The bullet is stopped by the bloclc, and the entire system swings up to a height h. It is possible to obtain the initial speed of the bullet by measuring a and the two masses. As an example of the technique, assume that the mass of the bulletr m1, is 4.61 g, the mass of the pendulum, m2, is 1.045 kg, and I: is 5.01 cm. (a) Find the velocity of the system after the bullet embeds in the block. E... [b] Calculate the initial speed of the bullet. EXERCISE HINTS: GETTING STARTED I I'M STUCK! A bullet with mass 5.46 g is fired horizontally into a 2.041-kg block attached to a horizontal spring. The spring has a constant 5.60 x 102 me and reaches a maximum compression of 6.48 cm. (a) Find the initial speed of the bulletblock system. my's [b] Find the speed of the bullet. mfs In a Broadway performante, an $3.0er actor swings From a R : 4.201714ng cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55 07kg costar in an inelastic collision. what maximum height do they reach after their upward swing? X Your response differs from the correct answer by more than 10%. Double check your calculations m Need Help? @