a metal bar 70cm long and 4.00 kg in mass supported on two knief -edge placed 10 cm from each end. a 6.00 kg weight is suspended at 30 cm from one end . find the reaction at the knife-edge ?
55N,43N
To find the reaction at the knife-edge, we will need to consider the equilibrium of the metal bar. We can start by calculating the center of mass of the metal bar.
Given that the metal bar is 70 cm long and the two knife-edges are placed 10 cm from each end, we can determine the length of the bar on each side of the knife-edges.
Length of the left portion of the bar = 10 cm
Length of the right portion of the bar = 70 cm - 10 cm = 60 cm
Next, we can calculate the center of mass using the principle of moments. This principle states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments in a system in equilibrium. The moment of an object is calculated by multiplying its weight by the distance from a reference point.
Let's take the left knife-edge as the reference point:
Clockwise moments:
Weight of the left portion (10 cm from the reference point) = Mass x Gravity x Distance = 4 kg x 9.8 m/s^2 x 10 cm
Weight of the right portion (70 cm from the reference point) = Mass x Gravity x Distance = 4 kg x 9.8 m/s^2 x 70 cm
Anticlockwise moments:
Weight of the suspended weight (30 cm from the reference point) = Mass x Gravity x Distance = 6 kg x 9.8 m/s^2 x 30 cm
Since the bar is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments:
4 kg x 9.8 m/s^2 x 10 cm + 4 kg x 9.8 m/s^2 x 70 cm = 6 kg x 9.8 m/s^2 x 30 cm
Now, let's solve this equation to find the reaction at the knife-edge.
4 kg x 9.8 m/s^2 x 10 cm + 4 kg x 9.8 m/s^2 x 70 cm = 6 kg x 9.8 m/s^2 x 30 cm
392 N cm + 2744 N cm = 1764 N cm
3136 N cm = 1764 N cm
Dividing both sides by 1110 N cm, we get:
3136 N / 1110 cm = 1764 N / 1110 cm
2.82 N ≈ 1.59 N
Therefore, the reaction at the knife-edge is approximately 1.59 N.