Solving for Acceleration and Friction on an Inclined Plane

AI Thread Summary
The problem involves a 2.91 kg block sliding down a 32° incline, requiring calculations for acceleration, the coefficient of kinetic friction, and the frictional force. To find the acceleration, the kinematic equation s = ut + (1/2)at² is applied, where the initial velocity (u) is zero. The weight of the block is resolved into components parallel and perpendicular to the incline, which are essential for determining the forces acting on the block. The discussion emphasizes the need to understand these components to calculate the frictional force and the block's final speed after sliding 1.98 m. Proper application of Newton's second law is crucial for solving the problem effectively.
mickjagger
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Applying Newton's 2nd law?!

Homework Statement



A 2.91 kg block starts from rest at the top of a 32◦ incline and slides 1.98 m down the incline in 1.28 s.
The acceleration of gravity is 9.8 m/s2

What is the acceleration of the block?
Answer in units of m/s2

What is the coefficient of kinetic friction be-
tween the block and the incline?

What is the frictional force acting on the
block?
Answer in units of N.

What is the speed of the block after it slid the
1.98 m? answer in m/s




Homework Equations


Newtons 2nd's Law

max=\sumfx=mgsin\Theta

0=\sum Fy=-mgcos\Theta+n


The Attempt at a Solution


I have no idea how to approach this problem.
 
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The weight of the block can be split into two components, one parallel to the plane and one perpendicular to the plane.

What the component parallel to the plane and what is the component perpendicular to the plane?
 


The thing to realize is that acceleration is change of velocity over time, and can be related to both velocity and distance.
I would assume that the acceleration is smooth, and apply the old formula

s=ut+(1/2)at^2 [s=distance, u=initial velocity, a= acceleration]

Then I would be able to derive the acceleration that was felt by the block while it slid down the plane, which is a good start.
 


using Vx=V cos Theta and Vy=Vsin theta:
x component= 1.679?
y component= 1.0492?
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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