A uniform rod of mass 50g
is supported horizontally on tow knife edges placed 10cm from its ends,what will be the reactions t these support, when a mass 100g is supported 10cm from the end point of the
rod.
explain this quastion
I get the mass of the rod is at the 50 cm point. I get that the two knife edges are 10 cm from each of its ends. I read that a mass of 100 g is also 10 cm from one end (which is exactly on the knife edge). All this is leads to a question which you did not ask.
To determine the reactions at the supports, we need to consider the balance of forces acting on the rod.
Let's label the left support as Support A, the right support as Support B, and the point where the 100g mass is supported as Point C.
First, let's find the center of mass of the rod. Since the rod is uniform, the center of mass will be at the midpoint of the rod. The distance from Support A to the center of mass is 10cm, and the distance from Support B to the center of mass is also 10cm.
Now, let's consider the forces acting on the rod. At Support A, there will be an upward reaction force (A_r) and a clockwise moment due to the weight of the rod and the 100g mass. At Support B, there will be an upward reaction force (B_r) and a counterclockwise moment due to the weight of the rod and the 100g mass.
To balance the moments around Support A, the clockwise moment must be equal to the counterclockwise moment. The clockwise moment is given by the weight of the rod (m_rod * g) multiplied by the distance from the center of mass to Support A (10cm). The counterclockwise moment is given by the weight of the 100g mass (m_100g * g) multiplied by the distance from Point C to Support A (10cm). Setting these two equal, we have:
m_rod * g * 10cm = m_100g * g * 10cm
Simplifying, we can cancel out the "g" and "10cm" terms:
m_rod = m_100g
Since the mass of the rod is given as 50g, we can substitute this value back in:
50g = m_100g
Therefore, the mass of the 100g mass is 50g.
Now that we have determined the mass of the 100g mass, we can find the reactions at the supports. The total weight of the rod and the 100g mass is:
Weight = (m_rod + m_100g) * g
Substituting in the values:
Weight = (50g + 50g) * g = 100g * g
Since the rod is horizontally supported, the total weight is balanced by the sum of the reactions at Support A and Support B:
A_r + B_r = Weight
Substituting in the value of the total weight:
A_r + B_r = 100g * g
So the reactions at the supports are equal and each equal to 100g * g / 2.
Please note that when calculating with units like grams, it is important to convert them to kilograms (kg) in order to obtain consistent units.