An 845 N sled is pulled a distance of 180 m. The task requires 1.38 x 104 J of work and is done by pulling on a rope with a force of 122 N. The rope is held at _____° above the horizontal.
To find the angle above the horizontal at which the rope is held, we can use the concept of work done.
The work done on an object can be calculated using the following formula:
Work = Force * Distance * Cosine(angle)
In this case, we know the work done (1.38 x 10^4 J), the force applied (122 N), and the distance (180 m). We need to find the angle.
Let's rearrange the formula to solve for the angle:
Angle = Arccos(Work / (Force * Distance))
Substituting the given values:
Angle = Arccos(1.38 x 10^4 J / (122 N * 180 m))
Calculating the value:
Angle ≈ Arccos(1.38 x 10^4 J / 21960 N.m) ≈ 61.8°
Therefore, the rope is held at approximately 61.8° above the horizontal.
To find the angle at which the rope is held, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done on the sled can be calculated using the formula:
Work = Force x Distance x Cos(θ)
Where:
- Work is the amount of work done on the sled (1.38 x 10^4 J)
- Force is the force applied on the sled (122 N)
- Distance is the distance over which the sled is pulled (180 m)
- θ is the angle between the direction of the force and the direction of motion of the sled (unknown)
We can rearrange the formula to solve for the angle:
θ = acos(Work / (Force x Distance))
Now let's plug in the values:
θ = acos(1.38 x 10^4 J / (122 N x 180 m))
Calculating this using a calculator, we get:
θ ≈ acos(1.138)
θ ≈ 46.3°
Therefore, the rope is held at approximately 46.3° above the horizontal.
Work = 13800 J = F*cosA*180m
F = 122 N
Solve for cosA, and get the angle A from that.
I get 51 degrees