Concept explainers
The angle of inclination of the plane on which a skateboarder rolls down.
Answer to Problem 52P
Solution:
The skateboarder rolls down an incline at an angle 120
Explanation of Solution
A skateboarder of mass m, rolls down an incline of length s, with an initial speed, in a time t. There is no friction between the incline and the skate board. The plane of the incline is at an angle to the horizontal.
The forces acting on the skateboarder is shown in the diagram below.
The weight mg of the skateboarder acts vertically downwards. The normal force acts perpendicular to the incline. The weight mg is resolved into two components, parallel and perpendicular to the incline.
The skateboarder accelerates with an acceleration a downwards under the action of the component of weight .
……(1)
By Newton’s second law,
……(2)
From equations (1)and (2),
……(3)
If the skateboarder rolls down the incline of length s in a time t, use the equation of motion,
Using the expression for acceleration found in equation (3)in the above expression and simplifying for .
Given:
The initial speed of the skateboarder
The length of the incline
Time taken to slide down the incline .
Formula used:
Calculation:
Substitute the given values in the equation and calculate the value of .
Calculate the angle of incline .
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