a 1.0 N-weight is hanging at rest as shown. In each case, write in the magnitude of the unknown force.
a) chain with a weight of 2.5 N has a 1.0 N hanging weight
b) chain with a weight of .5 N has a 1.0 N hanging weight
c) stretched elastic band with negligible weight has a 1.0 N hanging weight
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a) To determine the magnitude of the unknown force, we need to ensure that the system is in equilibrium. In this case, the weight of the hanging weight (1.0 N) and the weight of the chain (2.5 N) need to balance each other out.
The unknown force can be calculated as the difference between the weight of the chain and the weight of the hanging weight:
Unknown force = Weight of chain - Weight of hanging weight
Unknown force = 2.5 N - 1.0 N = 1.5 N
Therefore, the magnitude of the unknown force is 1.5 N.
b) Similar to case a), we need to find the magnitude of the unknown force that balances out the system. Given that the weight of the chain is 0.5 N and the weight of the hanging weight is 1.0 N, the unknown force can be calculated as:
Unknown force = Weight of chain - Weight of hanging weight
Unknown force = 0.5 N - 1.0 N = -0.5 N
The negative sign indicates that the unknown force is in the opposite direction compared to the hanging weight. Therefore, the magnitude of the unknown force is 0.5 N.
c) In this case, the stretched elastic band with negligible weight exerts an unknown force that needs to balance out the hanging weight of 1.0 N. The unknown force from the stretched elastic band will be equal in magnitude but opposite in direction to the hanging weight.
Therefore, the magnitude of the unknown force exerted by the stretched elastic band is also 1.0 N.
To solve these problems, we need to analyze the forces acting on the hanging weight in each case.
a) In the first case, a chain with a weight of 2.5 N is connected to a 1.0 N hanging weight. Since the chain is at rest, the forces acting on it must be balanced.
The gravitational force acting on the 2.5 N weight is equal to its weight, which is 2.5 N. This force is transmitted through the chain to the hanging weight.
In addition, there must be an upward force equal to the weight of the hanging weight (1.0 N) to balance the downward force.
Therefore, the unknown force in this case is 1.0 N upwards, as there must be a force of 1.0 N acting in the opposite direction to balance the system.
b) In the second case, a chain with a weight of 0.5 N is connected to a 1.0 N hanging weight. Once again, the forces acting on the chain must be balanced for it to be at rest.
The gravitational force acting on the 0.5 N weight is equal to its weight, which is 0.5 N. This force is transmitted through the chain to the hanging weight.
Similar to the previous case, there must be an upward force equal to the weight of the hanging weight (1.0 N) to balance the downward force.
Thus, the unknown force in this case is 1.0 N upwards, as there must be a force of 1.0 N acting in the opposite direction to maintain equilibrium.
c) In the third case, a stretched elastic band with negligible weight is attached to a 1.0 N hanging weight. Since the elastic band has negligible weight, we can ignore it for the purpose of this analysis.
The gravitational force acting on the 1.0 N hanging weight is once again 1.0 N downwards.
To balance this force and maintain equilibrium, there must be an equal and opposite force acting in the upward direction. Thus, the unknown force in this case is 1.0 N upwards.
In summary, the magnitude of the unknown force in all three cases is 1.0 N upwards.