A child holds a sled on a frictionless, snow-
covered hill, inclined at an angle of 29◦.
If the sled weighs 61 N, find the force ex-
erted on the rope by the child.
Answer in units of N.
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To find the force exerted on the rope by the child, we need to analyze the forces acting on the sled.
First, let's understand the forces involved:
1. Weight of the sled (acting vertically downward): This is the force due to gravity and is given as 61 N.
2. Normal force (acting perpendicular to the surface of the hill): This force cancels out the vertical component of the weight of the sled since the sled is on a frictionless hill. The normal force is equal in magnitude but opposite in direction to the weight of the sled.
Since the hill is frictionless, there is no horizontal force acting on the sled. Thus, the only horizontal force is the force exerted on the sled by the rope.
We can use trigonometry to determine the components of the weight of the sled along and perpendicular to the hill.
The weight of the sled can be broken down into its components as follows:
Weight of the sled perpendicular to the hill = Weight of the sled × cos(θ)
Weight of the sled along the hill = Weight of the sled × sin(θ)
where θ is the angle of the hill, given as 29°.
Now, we can find the force exerted on the rope by the child, which is equal in magnitude but opposite in direction to the weight of the sled along the hill.
Force exerted on the rope = Weight of the sled along the hill = Weight of the sled × sin(θ)
Substituting the given values:
Force exerted on the rope = 61 N × sin(29°)
Calculating the result:
Force exerted on the rope ≈ 29.4 N
Therefore, the force exerted on the rope by the child is approximately 29.4 N.