When a toy car is rapidly scooted across the floor, it stores energy in a flywheel. The car has mass 0.180 kg, and its flywheel has moment of inertia 4.00 × 10?5kg · m2. The car is 15.0 cm long. An advertisement claims that the car can travel at a scale speed of up to 700 km/h (440 mi/h). The scale speed is the speed of the toy car multiplied by the ratio of the length of an actual car to the length of the toy. Assume a length of 3.0 m for a real car. (a) For a scale speed of 700 km/h, what is the actual translational speed of the car? (b) If all the kinetic energy that is initially in the flywheel is converted to the translational kinetic energy of the toy, how much energy is originally stored in the flywheel? (c) What initial angular velocity of the flywheel was needed to store the amount of energy calculated in part (b)?
Solution 66P Introduction We have to calculate the ratio of the length of the toy car to real car. Then we can calculate the speed of the car. Now knowing the mass of the car we can calculate the kinetic energy required by the toy car to move with such speed. Finally equating the kinetic energy to the energy stored in flywheel, we can calculate the angular velocity of the flywheel. Step 1 The ratio of the length of toy car to the length of real car is 15.0 cm 15.0×10m r = 3.0 m = 3.0 m = 0.050 Hence the speed of the toy car is v toy= (700 km/h)r = (700 km/h)0.050 = 35.0 km/h = 9.72 m/s Hence the actual translational speed of the toy car is 9.72 m/s. Step 2 The kinetic energy of the toy car is K = mv = (0.180 kg)(9.72 m/s) = 85.0 J 2 2 Since the translational kinetic energy of the toy car is 85.0 J, the energy stored in the flywheel should be 85.0 J.