a horizontal beam 6.8m long of mass 15kg is supported by pillars of 0.2 of each end. There is a man of mass 85 kg standing 1.7kg from one end of the beam .draw a diagram showing the forces acting on the beam in this equilibrium condition .calculate the magnitudes of the loads carried by each support.
To draw a diagram showing the forces acting on the beam in equilibrium, we need to identify the different forces acting on the beam.
First, let's consider the weight of the beam itself. The weight of an object can be calculated using the formula: weight = mass x gravitational acceleration.
Given:
- Mass of the beam = 15 kg
- Gravitational acceleration (approximated as 9.8 m/s^2)
Weight of the beam = 15 kg x 9.8 m/s^2 = 147 N
Next, let's consider the weight of the man standing on the beam. Similarly, we can calculate the weight of the man using the same formula.
Given:
- Mass of the man = 85 kg
Weight of the man = 85 kg x 9.8 m/s^2 = 833 N
Now, let's draw the diagram:
<--- 1.7 m ---> <--- 4.9 m --->
o-----------------o------------------o
| |
| |
Beam Beam
Support Support
The left-most side of the beam represents the side where the man is standing. The distance of 1.7 m indicates the man's position from the support on that side.
Now, let's calculate the magnitudes of the loads carried by each support:
Since the beam is in equilibrium, the sum of the clockwise moments should be equal to the sum of the anticlockwise moments. The moments can be calculated using the formula: moment = force x distance.
For the equilibrium condition:
Clockwise moment = Anticlockwise moment
Let's consider the support on the man's side:
Clockwise moment = Weight of the beam x distance from the support
Anticlockwise moment = Weight of the man x distance from the support
Let's assume the support on the man's side carries a load of F1, and the support on the opposite side carries a load of F2.
Clockwise moment: F1 x 4.9 m
Anticlockwise moment: Weight of the man x 1.7 m
Therefore, we can write the equation: F1 x 4.9 m = 833 N x 1.7 m
From this equation, we can solve for F1:
F1 = (833 N x 1.7 m) / 4.9 m
Similarly, we can calculate the load carried by the support on the opposite side (F2), which is the weight of the beam minus F1.
F2 = Weight of the beam - F1
Substituting the values, we can calculate F2.
Once we have calculated the values of F1 and F2, we can determine the magnitudes of the loads carried by each support in the equilibrium condition.