A metal ball weighing 490 N hangs from a uniform heavy-duty chain weighing 245 N. (a) Find the force exerted by the chain on the ball. (b) Find the tension in the upper end of the chain. (c) Find the tension halfway from the upper end of the chain.
To find the force exerted by the chain on the ball, you need to consider the weight (force due to gravity) of the ball and the weight of the chain.
(a) The force exerted by the chain on the ball is equal to the weight of the ball. So, the force exerted by the chain on the ball is 490 N.
(b) To find the tension in the upper end of the chain, you need to consider the equilibrium of forces at that point. The forces acting at the upper end of the chain are the tension in the chain and the weight of the chain. Since the chain is in equilibrium, the tension in the chain is equal to the weight of the chain.
The weight of the chain is 245 N, so the tension in the upper end of the chain is also 245 N.
(c) To find the tension halfway from the upper end of the chain, you can consider the equilibrium of forces at that point. The forces acting at the halfway point of the chain are the tension in the chain, the weight of the chain, and the weight of the ball.
Since the chain is in equilibrium, the sum of the forces acting on it must be zero. The tension in the chain at the halfway point can be found by subtracting the weight of the chain and the weight of the ball from the tension in the upper end of the chain.
Tension at halfway point = Tension in upper end - Weight of chain - Weight of ball
Tension at halfway point = 245 N - 245 N - 490 N
Tension at halfway point = -490 N (Note: The negative sign indicates that the tension is directed downwards)
So, the tension halfway from the upper end of the chain is -490 N.