MHB Calculating Kinetic Energy of a Block on an Inclined Plane

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To calculate the speed of a 9kg block on a frictionless inclined plane of 4m, the initial gravitational potential energy is converted to kinetic energy at the bottom. The total initial energy is determined by the height of the incline, which can be calculated using the ramp length and angle. When a frictional force of 2 Newtons opposes the motion, the final speed must account for the work done against this force. The discussion emphasizes the importance of equating initial and final energies to solve for the block's speed under both scenarios. Understanding these energy transformations is crucial for solving the problem effectively.
Teh
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A block of mass 9kg is initially at rest at the top of an inclined plane of ramp length 4m.

-Assuming that the plane is frictionless, calculate the speed of the block at the bottom of the plane.

-Now instead assume the a frictionless force of Ffr = 2 Newtons opposes the motion of the block. Calculate the speed of the block at the bottom of the planeView attachment 5601I am stuck may anyone help me?
 

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Okay, first you need to compute the initial energy of the block, and the final energy of the block, and equate the two since there are no non-conservative forces at work.

Initially, the block has no kinetic energy, but it has gravitational potential energy. Can you give the total initial energy?
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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