A box is pushed across a floor with a force of 2.8 N at an angle of 26.8 degrees above the horizontal. How much work, in Joules, must be done to move the box a distance of 8.3 m?
Work = Fx*d = 2.8*Cos26.8 * 8.3 =
To determine the work done to move the box, we need to calculate the dot product between the applied force and the displacement of the box. The formula for work is:
Work = Force * Distance * cosθ
Where:
- Work is the work done (in Joules)
- Force is the applied force (in Newtons)
- Distance is the distance moved by the box (in meters)
- θ is the angle between the force and the displacement
In this case, the applied force is 2.8 N, and the distance moved by the box is 8.3 m. The angle θ is 26.8 degrees. However, we need to convert the angle to radians before calculating the cosine:
θ (in radians) = θ (in degrees) * π / 180
Let's calculate the angle in radians:
θ (in radians) = 26.8 * π / 180
Now, we can calculate the work done:
Work = 2.8 N * 8.3 m * cos(26.8 * π / 180)
Using a calculator, we can find the cosine of the angle and substitute it into the equation:
Work = 2.8 N * 8.3 m * cos(0.467)
After evaluating the expression, we can determine the work done.