A block of mass $20{\text{ }}kg$ is pulled from the bottom to the top of a slope. The slope has length $10{\text{ }}m$ and is inclined at ${4.5^ \circ }$ to the horizontal. The speed of the block is $2.5{\text{ }}m{\text{ }}{s^{ - 1}}$ at the bottom of the slope and $1.5{\text{ }}m{\text{ }}{s^{ - 1}}$ at the top of the slope.
a) Find the loss of kinetic energy and the gain in potential energy of the block.
b) Given that the work done against the resistance to motion is $50{\text{ }}J$, find the work done by the pulling force acting on the block.
c) Given also that the pulling force is constant and acts at an angle of ${15^ \circ }$ upwards from the slope, find its magnitude.
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