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.
the weight down the hill is mgSinTheta due to gravity.
the child has to counter that force.
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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 draw a free-body diagram to represent the sled.
^
/
/
________
| |
| sled |
| |
|________|
|
|
rope
In this case, there are two forces acting on the sled: the force of gravity (weight) and the force exerted by the child on the rope.
1. Weight of the sled:
The weight of the sled is given as 61 N. The force of gravity always acts vertically downward, so we can represent it as a vector pointing downwards with a magnitude of 61 N.
2. Force exerted on the rope by the child:
The force exerted by the child on the rope is directed along the rope, perpendicular to the slope of the hill. Let's call this force "T". We need to determine the magnitude of this force.
To find the force exerted on the rope by the child, we need to resolve the weight of the sled into two components: one perpendicular to the slope and one parallel to the slope.
The perpendicular component of the weight is given by:
W_perpendicular = Weight * sin(angle)
W_perpendicular = 61 N * sin(29°)
Now, since the sled is on a frictionless surface, the force exerted by the child on the rope is equal in magnitude and opposite in direction to the perpendicular component of the weight.
Therefore, the force exerted on the rope by the child (T) is:
T = W_perpendicular
T = 61 N * sin(29°)
Now we can calculate the force exerted on the rope by the child.
Using a calculator:
T ≈ 61 N * 0.481
T ≈ 29.541 N
So, the force exerted on the rope by the child is approximately 29.541 N.