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a constant force equal to (5i+2j)N moves a particle through a displacement S=(2i+3j). Calculate the workdone by the force. At what angle to the horizontal was the force applied?
The work done is the dot product of force and displacement vectors, which is
5*2 + 3*2 = 16 Joules
If the j component is up and the i component is horizontal, the force angle from the horizontal is arctan(2/5) = 21.8 degrees.
To calculate the work done by a force, we can use the formula:
Work = Force dot Product Displacement
Given that the force is (5i + 2j)N and the displacement is (2i + 3j), we can calculate the dot product by multiplying the corresponding components and summing them. The dot product is given by:
Force dot Product Displacement = (5 * 2) + (2 * 3) = 10 + 6 = 16
Therefore, the work done by the force is 16 N.
To calculate the angle at which the force was applied to the horizontal, we can use the formula:
Angle = arctan (Fy/Fx)
Where Fx is the force in the x-direction and Fy is the force in the y-direction.
Given that the force is (5i + 2j)N, we have Fx = 5 and Fy = 2. Plugging these values into the formula, we get:
Angle = arctan (2/5)
Using a calculator, we find that the angle is approximately 21.8 degrees.
Therefore, the force was applied at an angle of approximately 21.8 degrees to the horizontal.