An old streetcar rounds a flat corner of radius 9.1 m, at 16 km/h. What angle with the vertical will be made by the loosely hanging hand straps?
Question
An old streetcar rounds a flat corner of radius 9.1 m, at 16 km/h. What angle with the vertical will be made by the loosely hanging hand straps?
Solution
To solve this problem, we need to use the concept of centripetal acceleration and the force of gravity.
Step 1: Convert the speed from km/h to m/s 16 km/h = 16 * 1000/3600 = 4.44 m/s
Step 2: Calculate the centripetal acceleration Centripetal acceleration, a = v^2 / r a = (4.44 m/s)^2 / 9.1 m a = 2.18 m/s^2
Step 3: Calculate the angle The angle θ can be found using the equation tan(θ) = a / g, where g is the acceleration due to gravity (9.8 m/s^2). θ = tan^-1 (a / g) θ = tan^-1 (2.18 m/s^2 / 9.8 m/s^2) θ = 12.5 degrees
So, the loosely hanging hand straps will make an angle of 12.5 degrees with the vertical.
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