A force of 600N is applied to a metal box to pull it 15 m across a floor. The roped used to pull the box is held at an angle of 46 degrees with the floor. How much work is done? My answer is w= 6251.93J
Yes, that's what I got, also.
To calculate the work done in this scenario, we can use the formula:
Work = Force * Distance * cos(theta),
where theta is the angle between the force direction and the displacement direction.
Given:
Force = 600 N,
Distance = 15 m,
Theta = 46 degrees.
First, we need to calculate the component of the force in the direction of displacement. This can be found using trigonometry:
Force component in the direction of displacement = Force * cos(theta)
= 600 N * cos(46°)
Next, we can calculate the work done using the formula:
Work = Force component * Distance
= 600 N * cos(46°) * 15 m
Now we can evaluate this expression to find the work done:
Work = 600 N * 0.7193 * 15 m
= 6492.9 J
Therefore, the correct value for the work done is approximately 6492.9 Joules (J), not 6251.93 J as you mentioned.
To calculate the work done, we can use the formula:
Work = Force × Distance × cosθ
Where:
- Force is the applied force (600N in this case),
- Distance is the distance traveled (15m in this case), and
- θ is the angle between the force and the direction of motion (46 degrees in this case).
First, let's find the value of cosθ.
cosθ = cos(46 degrees) = 0.71934 (rounded to 5 decimal places)
Now, we can substitute the values into the formula:
Work = 600N × 15m × 0.71934
Work = 6474.06 Joules (rounded to 2 decimal places)
So, the correct answer is approximately 6474.06J, not 6251.93J.