A box is pushed by a 750 N force that acts at a 30 degree angle with a friction less surface.The force pushes a box that has a weight of 500N a distance of 15 meters. How much work is done on the box?
work=force*distance*cosTheta
= 759*15*cos30
To find the work done on the box, you can use the formula:
Work = Force × Distance × cosθ
Where:
- Work is the amount of work done (in joules, J).
- Force is the magnitude of the force applied (in newtons, N).
- Distance is the distance over which the force is applied (in meters, m).
- θ is the angle between the force and the direction of motion (in degrees).
In this case, the force applied is 750 N, the distance is 15 meters, and the angle is 30 degrees. The weight of the box (500 N) can be ignored since it is not relevant for calculating the work done on the box.
Now, let's calculate the work done:
Work = 750 N × 15 m × cos(30°)
First, convert the angle from degrees to radians:
θ (in radians) = θ (in degrees) × (π/180)
θ (in radians) = 30° × (π/180) = π/6 rad
Now, substitute the values into the formula:
Work = 750 N × 15 m × cos(π/6)
Calculating the cosine of π/6:
cos(π/6) ≈ 0.866
Work ≈ 750 N × 15 m × 0.866
Finally, calculate the work:
Work ≈ 9705 J
Therefore, the work done on the box is approximately 9705 joules.
To find the work done on the box, you need to calculate the dot product between the applied force and the displacement of the box.
The dot product formula is given by:
W = F · d · cos(θ)
Where:
W = work done
F = applied force
d = displacement
θ = angle between the force and displacement vectors
In this case, the applied force is 750 N, the displacement is 15 meters, and the angle between the force and displacement vectors is 30 degrees.
Plugging in the values:
W = 750 N × 15 m × cos(30°)
To find the cosine of 30 degrees, you can use a calculator or look up the value. It is approximately 0.866.
W = 750 N × 15 m × 0.866
W = 9592.5 Joules
Therefore, the work done on the box is approximately 9592.5 Joules.