adv_rot

Name: _____________________________________________Block: _____________Date: ______________ Mr. Almeida Honors Physics 1.2.3. 4.5.6. ADVANCED ROTATIONAL MOTION PROBLEMS 1. An air puck of mass 0.2 kg is tied to a string and allowed to revolve in a circle of radius 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.0 kg is tied to it as shown in Fig. 1. The suspended mass remains in equilibrium while the puck on the tabletop revolves. a. What is the tension in the string? b. What is the horizontal force on the puck? c. What is the speed of the puck? a. b. c. 2. A roller-coaster vehicle has a mass of 500 kg when fully loaded with passengers (Fig. 2).a. If the vehicle has a speed of 20.0 m/s at point A, what is the force of the track on the vehicle at this point? b. What is the maximum speed the vehicle can have at point B in order for gravity to hold it on the track? a. b. 3. In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation at an angular speed of 5.00 rad/s, as in Fig. 3. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between the riders clothing and the wall is needed to keep the rider from slipping? (Hint: Recall that the magnitude of the maximum force of static friction is equal to N, where N is the normal force in this case, the force causing the centripetal motion. ADVANCED ROTATIONAL MOTION PROBLEMS 4. A skier starts at rest at the top of a large hemispherical hill (Fig. 4). Neglecting friction, show that the skier will leave the hill and become airborne at a distance h = R/3 below the top of the hill. (Hint: At this point, the normal force goes to zero. 5. A 0.50-kg ball that is tied to the end of a 1.5-m light cord is revolved in a horizontal plane, with the cord making a 30 angle with the vertical (Fig. 5).a. Determine the balls speed. b. If, instead, the ball is revolved so that its speed if 4.0 m/s, what angle does the cord make with the vertical? c. If the cord can withstand a maximum tension of 9.8 N, what is the highest speed at which the ball can move? 6. A massless spring of constant k = 78.4 N/m is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it a distance d, as in Fig. 6. The block (initially at rest) is then released and travels toward a circular loop-the-loop of radius R = 1.5 m. The entire track and the loop-the-loop is frictionless, except for the section of track between points A and B. Given that the coefficient of kinetic friction between the block and the track along AB is k = 0.30, and that the length of AB is 2.5 m, determine the minimum compression d of the spring that enables the block to just make it through the loop-the-loop at point C. (Hint: The force exerted by the track on the block will be zero if the block barely makes it through the loop-the-loop.