Concept explainers
(a) To Determine:
The acceleration of the block sliding down an inclined plane.
Answer to Problem 55P
Solution:
The acceleration of the block down the inclined plane is found to be 3.7 m/s2.
Explanation of Solution
A block starting from rest slides down a distance s along the length of the incline which is at an angle and attains a speed v.
The free body diagram for the block is shown in the diagram below.
The weight mg of the block 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 block experiences a force due to the component of weight and is accelerated at the rate a.
……(1)
By Newton’s second law,
……(2)
From equations (1)and (2),
……(3)
Given:
The initial speed of the block
The angle of the incline
The distance traveled by the block down the incline
Formula used:
Calculation:
Substitute the given value of and 9.8 m/s2 for g in the equation for acceleration
(b) To Determine:
The speed of the block when it reaches the end of the incline.
Answer to Problem 55P
Solution:
The speed of the block when it reaches the end of the inclined plane is 9.4 m/s.
Explanation of Solution
To calculate the speed of the block when it reaches the end of the incline, use the equation of motion,
Given:
The initial speed of the block
The angle of the incline
The distance traveled by the block down the incline
Formula used:
Calculation:
Substitute the values of , a and s in the equation to calculate the speed of the block when it reaches the end of the inclined plane.
The speed of the body when reaches the end of the incline is calculated using the equation of motion and is found to be 9.4 m/s.
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Physics: Principles with Applications
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