A 55-kg packing crate is pulled with constant speed across a rough floor with a rope that is at an angle of 44.7 degrees above the horizontal.
If the tension in the rope is 155 N, how much work is done on the crate to move it 9.0 m?
*looking for W=__J
work= 155*9*cos44.7
To find the work done on the crate, we can use the equation:
Work = Force × displacement × cos(θ)
Where:
- Work is the amount of work done on the crate.
- Force is the tension in the rope, which is given as 155 N.
- Displacement is the distance the crate is moved, which is given as 9.0 m.
- θ (theta) is the angle between the force and the displacement. In this case, it is 44.7 degrees.
Now, let's plug in the given values into the equation:
Work = 155 N × 9.0 m × cos(44.7°)
To calculate cos(44.7°), we can use a calculator:
cos(44.7°) ≈ 0.707
Substituting the value back into the equation:
Work ≈ 155 N × 9.0 m × 0.707
Finally, we can calculate the work:
Work ≈ 978 J
Therefore, the amount of work done on the crate to move it 9.0 m is approximately 978 Joules (J).
To find the work done on the crate, we can use the equation:
Work = Force x Distance x cos(angle)
In this case, the force is the tension in the rope (155 N), the distance is the distance the crate is moved (9.0 m), and the angle is 44.7 degrees.
First, we need to convert the angle to radians:
angle (in radians) = angle (in degrees) x π / 180
angle (in radians) = 44.7 x π / 180
angle (in radians) = 0.78 radians
Now we can substitute the values into the equation:
Work = 155 N x 9.0 m x cos(0.78 radians)
Using a calculator, we find:
Work ≈ 1264.55 J
Therefore, the work done on the crate to move it 9.0 m is approximately 1264.55 J.