A force of magnitude 25Nis directed at an angle of 37 deg above the horizontal moves a 10 Kg block along a horizontal surface at a constant velocity .How much work is done by this force in moaing the block a distance of 15m?
work=force x distance where force is the amount of force directed in the direction of distance.
work=25cos37 x 15 joules
299.49 J
To find the work done by a force, we can use the equation:
Work = Force × Distance × cosθ
Where:
- Work is the work done by the force (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 direction of the force and the direction of motion (in degrees)
In this case, we have:
- Force = 25N
- Distance = 15m
- θ = 37°
Let's plug in the values into the equation to calculate the work done:
Work = 25N × 15m × cos(37°)
To find the cosine of 37°, we can use a calculator:
cos(37°) ≈ 0.7986
Now we can substitute the value into the equation:
Work = 25N × 15m × 0.7986
Simplifying the equation:
Work ≈ 299.575 J
Therefore, the work done by the force in moving the block a distance of 15m is approximately 299.575 joules.
To find the work done by a force, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of work done by the force (in joules, J)
- Force is the magnitude of the force (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 has a magnitude of 25N and is directed at an angle of 37 degrees above the horizontal. The block is being moved along a horizontal surface, so the angle between the force and the direction of motion is 0 degrees.
Substituting the values into the formula:
Work = 25N × 15m × cos(0)
Since the cos(0) is equal to 1, the equation simplifies to:
Work = 25N × 15m
Calculating further:
Work = 375 J
Therefore, the work done by this force in moving the block a distance of 15m is 375 joules.