a child holds a sled at rest on a frictionless snow covered hill. if the sled weighs 77newtons. find the force exerted on the rope by the child and the force on the rope exerted by the sled by the hill?
This is impossible to answer without knowing the incline of the slope,
For an incline angle of θ, the force exerted by the rope on the child is: 77N sin(θ).
To solve this problem, we need to consider the forces acting on the sled and the child holding onto the sled.
1. Force exerted on the rope by the child:
Since the sled is at rest, the force exerted on the rope by the child must be equal but opposite to the force exerted on the sled by the hill. This can be calculated using Newton's second law (F = ma), where the acceleration is zero because the sled is at rest.
Therefore, the force exerted on the rope by the child is equal to the weight of the sled:
Force exerted on the rope by the child = Weight of the sled = 77 Newtons.
2. Force exerted on the rope by the sled:
The force exerted on the rope by the sled can be calculated using the same logic as above. Since the sled is at rest, there is no net force acting on it, and hence the force exerted on the rope by the sled must be equal but opposite to the force exerted on the rope by the child.
Therefore, the force exerted on the rope by the sled is also equal to the weight of the sled:
Force exerted on the rope by the sled = Weight of the sled = 77 Newtons.
So, both the force exerted on the rope by the child and the force exerted on the rope by the sled are 77 Newtons.
To find the force exerted on the rope by the child and the force on the rope exerted by the sled, we need to consider the forces acting on the sled.
1. Force exerted by the child on the rope:
When the child holds the sled at rest, the force exerted by the child on the rope directly opposes the force of gravity acting on the sled. This force is equal in magnitude but opposite in direction to the weight of the sled, which is 77 Newtons.
Therefore, the force exerted by the child on the rope is also 77 Newtons, directed upwards.
2. Force exerted on the rope by the sled due to the hill:
Since the hill is frictionless, there is no friction force acting on the sled. The only force acting on the sled (other than its weight) is the normal force exerted by the hill perpendicular to its surface.
According to Newton's third law of motion, the force exerted by the sled on the hill is equal in magnitude but opposite in direction to the normal force exerted by the hill on the sled.
Hence, the force on the rope exerted by the sled and the hill is also 77 Newtons, directed downwards.
So, to summarize:
- The force exerted on the rope by the child is 77 Newtons, directed upwards.
- The force on the rope exerted by the sled and the hill is 77 Newtons, directed downwards.