The differential gear of a car axle allows the wheel on the left side of a car t
ID: 2192581 • Letter: T
Question
The differential gear of a car axle allows the wheel on the left side of a car to rotate at a different angular speed than the wheel on the right side. A car is driving at a constant speed around a circular track on level ground, completing each lap in 20.8 s. The distance between the tires on the left and right sides of the car is 1.72 m, and the radius of each wheel is 0.330 m. What is the difference between the angular speeds of the wheels on the left and right sides of the car? ANSWER= RAD/SExplanation / Answer
1. The differential gear of a car axle allows the wheel on the left side of a car to rotate at a different angular speed than the wheel on the right side. A car is driving at a constant speed around a circular track on level ground, completing each lap in 23.8 s. The distance between the tires on the left and right sides of the car is 1.60 m, and the radius of each wheel is 0.340 m. What is the difference between the angular speeds of the wheels on the left and right sides of the car? 2. An object attached to a horizontal spring is oscillating back and forth along a frictionless surface. The maximum speed of the object is 2.00 m/s, and its maximum acceleration is 7.45 m/s2. How much time elapses between an instant when the object's speed is at a maximum and the next instant when its acceleration is at a maximum? If the outer tier A moves over a circle of radius R, the inner tier B moves over a circle of radius R - 1.6 Both takes the same time for one lap 23.8 s The angular speed of A = ?1 = 2p N1 --1 The angular speed of B = ?2 = 2p N2 ---2 Difference in speed = 2p r [N1 - N2] ===================================== In 23.8 second A moves a distance = circumference of its circle = 2p R In 23.8 second, the number of revolutions made by A = 2p R / 2p r = R /r In one second, the number of revolutions made by A = N1 = R / 23.8 r N2 = [R- 1.6] / 23.8 r] . 2p r [N1 - N2.] = 2p 1.6 / 23.8 r = 2p 1.6 / 23.8 *0.340 1.24 rad /s. ======================================… 2) Maximum acceleration = ?^2 A= 7.45 m/s^2 and Maximum velocity = ?A = 2 m/s Dividing the first by the second equation, ? = 7.45/2 = 3.725 rad /s T = 2p/ ? = 2p/ 3.725 = 1.69 s. This is for full oscillation. The question is T/4 = ? Answer = 0.42 s.