Question

A ____ kg block is dragged over a rough, horizontal surface by a constant force. Find the work done by the ___ N force. Options: A. 2.5 kg; 10 N B. 5.0 kg; 8 N C. 3.0 kg; 12 N D. 4.5 kg; 6 N

Answer 1

A 3.0 kg block is dragged over a rough, horizontal surface by a constant force of 12 N.

Step-by-step explanation:

To find the work done
`(\(W\))`, we use the formula
`\(W = F \cdot d \cdot \cos(\theta)\)`, where
`\(F\)` is the force applied,
`\(d\)` is the displacement, and
`\(\theta\)` is the angle between the force and displacement vectors. In this case, the force is given as 12 N, and assuming the force is applied horizontally,
`\(\cos(\theta)\)` is 1.

The work done is then calculated as
`\(W = 12 \, \text{N} \cdot d\)`, where
`\(d\)` is the displacement. The mass
`(\(m\))` is not directly required to find the work done, but it's given as 3.0 kg in the correct option for additional information.

Now, to choose the correct option, we look for the combination of mass and force that matches the given force of 12 N. Option C with a 3.0 kg mass and a force of 12 N satisfies this requirement. Therefore, the correct option is C.

In conclusion, the work done by the 12 N force on a 3.0 kg block is calculated using the formula
`\(W = F \cdot d\),` and the correct option is C, where the mass is 3.0 kg, and the force is 12 N.