A sled rope is held at an angle of 45 degrees with the horizontal ground. A force of 60 N acting parallel to the ground is required to keep the sled in motion. How much force must be exerted on the rope?
T=F/cosφ =60/0.707 =
=60/0.707 = 84.87 N
To find the force that must be exerted on the rope, we can use trigonometry. The force exerted on the rope can be found by determining the horizontal component of the force required to keep the sled in motion.
Given:
Angle between the sled rope and the horizontal ground (θ) = 45 degrees
Force required to keep the sled in motion (F_parallel to ground) = 60 N
To find the force exerted on the rope (F_exerted on rope), we need to determine the horizontal component of the force required to keep the sled in motion.
Using trigonometry, we can find the horizontal component using the formula:
Cos(θ) = Adjacent / Hypotenuse
In this case, the hypotenuse is the force required to keep the sled in motion, and the adjacent side is the horizontal component of the force.
Cos(45) = F_horizontal / F_parallel to ground
Now let's solve for F_horizontal:
F_horizontal = Cos(45) * F_parallel to ground
F_horizontal = Cos(45 degrees) * 60 N
Using a calculator, we can find:
F_horizontal ≈ 42.43 N
Therefore, the force that must be exerted on the rope is approximately 42.43 N.
To determine the force that must be exerted on the rope, we need to analyze the forces acting on the sled.
Let's break the force of 60 N into its components. Since the force is parallel to the ground, we can determine its horizontal and vertical components using trigonometry.
The horizontal component of the force (F_horizontal) can be found by multiplying the total force (60 N) by the cosine of the angle (45 degrees).
F_horizontal = 60 N * cos(45 degrees)
Similarly, the vertical component of the force (F_vertical) can be determined by multiplying the total force (60 N) by the sine of the angle (45 degrees).
F_vertical = 60 N * sin(45 degrees)
Now, since we want to find the force exerted on the rope, which is vertical, we need to focus on the vertical component of the applied force (60 N * sin(45 degrees)).
Thus, the force that must be exerted on the rope is equal to the vertical component of the applied force.
Therefore, the force that must be exerted on the rope is 60 N * sin(45 degrees).