A block sliding up a ramp, solve for acceleration

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A block sliding up a 50-degree ramp at an initial speed of 9 m/s experiences acceleration due to gravity and friction. The coefficient of kinetic friction is 0.51, and the initial calculations suggest an acceleration of -3.829 m/s², which is incorrect. The correct approach involves considering both the gravitational force component along the ramp and the frictional force acting against the block's motion. The discussion emphasizes the importance of accurately calculating these forces to determine the block's true acceleration. Understanding the interplay of gravity and friction is crucial for solving the problem correctly.
acid234
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Homework Statement


A block is sent sliding up a 50 degree ramp at an initial speed of 9m/s. The coefficient of kinetic friction between the ramp and the block is 0.51. Find the acceleration of the block.

Homework Equations


Fk = (Fn)uk
F=ma

The Attempt at a Solution


umgsin50 = ma
ugsin50 = a
0.51(-9.8)sin50 = a
a = -3.829

Which is far from the right answer.
 
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gravity! Think about if the block wasn't initially moving, would you know how to calculate its downward acceleration from gravity alone? The friction portion seems to be correct though.
 
Hi acid234, welcome to PF.
On the inclined plane, the retardation is caused by two factors. 1) Component of the weight along the inclined plane and 2) the frictional force. Find them
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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