Answer :
The work done by the weight of the box can be calculated using the formula:
Work = Force x Distance x Cosine(angle)
In this case, the force is equal to the weight of the box, which can be calculated using the formula:
Weight = Mass x Acceleration due to gravity
The mass of the box is given as 4.00 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
So, Weight = 4.00 kg x 9.8 m/s^2 = 39.2 N
The distance is given as 8.0 m, and the angle of the ramp is 30.0 degrees.
Now, we can calculate the work done by the weight of the box using the formula:
Work = 39.2 N x 8.0 m x Cos(30.0 degrees)
To find the cosine of 30.0 degrees, we can use a calculator or refer to a trigonometric table. The cosine of 30.0 degrees is approximately 0.866.
Work = 39.2 N x 8.0 m x 0.866 = 271.168 J
Therefore, the work done by the weight of the box is approximately 271.168 J.
The given answer choices are: 157 J, -157 J, +78.4 J, 78.4 J, -78.4 J.
None of the given answer choices match the calculated value of 271.168 J.
Therefore, none of the given answer choices is correct.
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