A chandelier is suspended by two identical, vertical chains side by side. The chandelier's mass is m = 5.3 kg.
A. If the tension in one chain is represented by T, write an expression for this tension in terms of m and g, the gravitational acceleration on the Earth's surface. Pick a coordinate system so that this tension is positive. T=?
B. What is the tension in one chain, T, in Newtons?
Steps only please and thank you for your help
A. T = mg
B. T = 5.3 kg * 9.8 m/s^2 = 51.94 N
A. To find the expression for the tension in one chain (T), you can start by considering the equilibrium of forces acting on the chandelier. Since the chandelier is suspended by two vertical chains, the tension in each chain will support its weight.
The weight of the chandelier can be calculated by multiplying its mass (m) by the gravitational acceleration (g). Therefore, the weight exerted downwards is given by W = m * g.
Since the chandelier is in equilibrium, the tension in each chain must balance this weight. Since the chains are identical, the tension in one chain is T.
So, the expression for the tension in one chain in terms of m and g is:
T = W = m * g
B. To calculate the tension in one chain (T) in Newtons, you can substitute the given values. First, determine the value of the gravitational acceleration on the Earth's surface, which is approximately 9.8 m/s^2.
Then, substitute the values:
T = m * g = 5.3 kg * 9.8 m/s^2
Now, calculate the tension in one chain:
T = 51.94 N
Therefore, the tension in one chain is approximately 51.94 Newtons.
A.
Step 1: Identify the forces acting on the chandelier. In this case, there are two chains supporting the chandelier, so the tension in one chain is a force acting upwards.
Step 2: Apply Newton's second law in the vertical direction. The sum of the forces in the vertical direction is equal to the mass times the acceleration. Since the chandelier is not moving vertically, the acceleration is zero. Therefore, the sum of the forces is also zero.
Step 3: The forces acting vertically are the tension in one chain (T) and the weight of the chandelier (mg). The weight acts downwards and is equal to the mass times the gravitational acceleration (mg).
Step 4: Use the equation from step 3 to write the expression for the tension in one chain:
T - mg = 0
Step 5: Rearrange the equation to solve for the tension in one chain (T):
T = mg
B.
Step 1: Substitute the given values into the expression from part A to calculate the tension in one chain:
T = m * g
Step 2: Substitute the given values for mass (m = 5.3 kg) and gravitational acceleration (g = 9.8 m/s^2) to calculate the tension in one chain:
T = 5.3 kg * 9.8 m/s^2
Therefore, the tension in one chain (T) is equal to 51.94 N.