A force of F = 125 N is used to drag a crate 3.0 m across a floor. The force is directed at an angle upward from the crate so the vertical part of the force is Fv = 65 N and the horizontal part of the force is Fh = 107 N. How much work is done on the box?
the work is done by the horizontal component ... f * d
got it
To find the work done on the box, we need to calculate the dot product of the force vector and the displacement vector. The dot product is given by:
Work = F * d * cos(theta)
where F is the magnitude of the force vector, d is the magnitude of the displacement vector, and theta is the angle between the force vector and the displacement vector.
In this case, the force vector is given as F = 125 N, the displacement is given as d = 3.0 m, and the angle theta can be determined using the components of the force vector.
First, let's find the angle theta:
tan(theta) = Fv / Fh
Substituting the given values:
tan(theta) = 65 N / 107 N
theta = arctan(65/107)
Using a calculator, we find:
theta ≈ 31.49 degrees
Now, we can calculate the work done:
Work = F * d * cos(theta)
Substituting the given values:
Work = 125 N * 3.0 m * cos(31.49 degrees)
Using a calculator, we find:
Work ≈ 327.08 Joules
Therefore, the work done on the crate is approximately 327.08 Joules.
To calculate the work done on the box, we need to use the formula:
Work = Force x Distance x cos(theta)
Where:
- Work is the amount of work done (in joules)
- Force is the applied force (in newtons)
- Distance is the displacement of the object (in meters)
- cos(theta) is the cosine of the angle between the applied force and the direction of displacement
In this case, the applied force has a vertical and horizontal component, but we are given the values for the vertical force (Fv = 65 N) and the horizontal force (Fh = 107 N).
Since the force is directed upward from the crate, the vertical component of the force (Fv) is responsible for moving the crate vertically against gravity, and thus does not contribute to the horizontal displacement. Therefore, we can ignore the vertical component (Fv) when calculating the work done on the box.
Now, let's calculate the work done:
Work = Fh x Distance x cos(theta)
Given that the horizontal force (Fh) is 107 N and the distance is 3.0 m, we can substitute these values into the formula:
Work = 107 N x 3.0 m x cos(theta)
However, we don't have the value of the angle (theta) between the applied force and the direction of displacement.
To find the angle (theta), we can use the relationship between the vertical and horizontal components of the force (Fv and Fh):
tan(theta) = Fv / Fh
Substituting the given values:
tan(theta) = 65 N / 107 N
Now, using the inverse tangent function (tan^(-1)), we can find the angle (theta):
theta = tan^(-1) (65 N / 107 N)
Evaluating this expression will give us the angle in radians.
Finally, substitute the calculated value of theta into the formula for work:
Work = 107 N x 3.0 m x cos(theta)
Calculating this expression will give us the work done on the box in joules.