You pull your little sister across a flat snowy field on a sled. Your sister plus the sled have a mass of 39 kg. The rope is at an angle of 39 degrees to the ground. As you pull with a force of 31 N, the sled travels a distance of 47 m.
To solve this problem, we can break it down into a few steps:
Step 1: Identify the given information.
- Mass of sister plus sled (m): 39 kg
- Force applied (F): 31 N
- Angle of the rope to the ground (θ): 39 degrees
- Distance traveled by the sled (d): 47 m
Step 2: Resolve the force into its horizontal and vertical components.
Since the force is acting at an angle to the ground, we need to resolve it into its horizontal and vertical components.
The horizontal component (Fh) can be calculated using the formula:
Fh = F * cos(θ)
The vertical component (Fv) can be calculated using the formula:
Fv = F * sin(θ)
Step 3: Calculate the work done.
The work done (W) can be calculated using the formula:
W = F * d * cos(θ)
Since the force is acting horizontally (parallel to the direction of motion), we use the horizontal component of the force in the formula.
Step 4: Substitute the values and calculate.
Substitute the values into the formulas and perform the calculations.
Fh = 31 N * cos(39°)
Fv = 31 N * sin(39°)
W = 31 N * 47 m * cos(39°)
By solving these equations, you can find the values of Fh, Fv, and W.