Solving Newton's Law Problem: Force on the Rope w/ 56N Sled

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To solve the problem of the force exerted on the rope by a child holding a 56 N sled on a 25-degree incline, the correct approach involves analyzing the forces acting on the sled. The sled's weight acts vertically downward, and the component of this weight along the incline is calculated using 56 N * sin(25). This downward force along the hill requires an equal force exerted by the child upward along the incline to maintain equilibrium. The initial calculation of 23.67 N is incorrect because it does not account for the need to balance the downward force. The correct force exerted on the rope by the child is therefore equal to the component of the sled's weight acting along the incline.
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Homework Statement



A child holds a sled on a frictionless, snow-covered hill, inclined at an angle of 25 degrees.If the sled weighs 56 N, find the force exerted on the rope by the child.

Homework Equations


\SigmaF=ma


The Attempt at a Solution


I set up a right triangle with 56N as the hypotenuse. I then figured the x component of force, or the force exerted on the rope by the child, to be 56sin25. I got 23.67N but when I submitted this it was wrong am I missing something here.

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That answer looks right to me.
The method is not. The 56 N acts straight down, and 56*sin(25) is the component acting downward along the hill. An equal force upward along the hill is needed to cancel it.
 
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