Question

A rope pulling a sled is sloped at 20.0° upward at the point of contact. The tension in the rope is 45 N. What is the horizontal component of the force?

Answer 1

The horizontal component of the force acting on the sled is 42.3 N.

The rope attached to the sled slopes upwards at an angle θ, as shown in the diagram.

The tension T in the rope acts along the length of the rope. Resolve the tension into two components along the horizontal and vertical directions.

The horizontal component of the tension is T cosθ.

Substitute 45 N for T and 20.0⁰ for θ.

$Tcos \theta =(45 N)(cos20.0^o)= 42.286 N=42.3 N$

The horizontal component of the force acting on the sled is 42.3 N.

Answer 2

Since the tension in the rope is 45 Newton, the horizontal component of the force acting on the sled is 42.29 Newton.

Given the following data:

• Angle of inclination = 20.0°

• Tension = 45 Newton

To find the horizontal component of the force acting on the sled:

Mathematically, the horizontal component of a force is given by the formula:

$F_y = Fcos(\theta)$

Substituting the given parameters into the formula, we have;

$F_y = 45cos(20)\\\\F_y = 45 \times 0.9397\\\\F_y = 42.29 \; Newton$

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