A dog is tugging forward on a leas held by a physics student who is standing still. The dog is tugging with a force of 63N. The student estimates the leash to be at an angle of 25 degrees above the ground. What is the tension in the leash?
That will depend upon whether the 63 N force applied by the dog is applied to the leash, or parallel to the ground by its legs. In the former case, the answer is 63N, regardless of angle.
To determine the tension in the leash, we can break down the force exerted by the dog into its horizontal and vertical components.
First, we calculate the vertical component of the force using the sine function:
Vertical Component = Force × sin(angle)
Vertical Component = 63 N × sin(25°)
Vertical Component = 26.84 N
Next, we calculate the horizontal component of the force using the cosine function:
Horizontal Component = Force × cos(angle)
Horizontal Component = 63 N × cos(25°)
Horizontal Component = 56.84 N
Since the student is standing still, the vertical component of the force is counterbalanced by the force exerted by the ground. Therefore, the tension in the leash is equal to the horizontal component of the force, which is 56.84 N.