A beam having a length of 20 metres is pivoted at its mid point. A 200 newton load is located at a point 5 m from the right hand end of the beam. A 300 newton load is located at a point 8 m from the right hand end. In order for the beam to be in equilibrium, what load is required at the extreme left end of the beam?

Question

A beam having a length of 20 metres is pivoted at its mid point. A 200 newton load is located at a point 5 m from the right hand end of the beam. A 300 newton load is located at a point 8 m from the right hand end. In order for the beam to be in equilibrium, what load is required at the extreme left end of the beam?

Answer 1

the moments must balance. That is, if a load of w is located 10m to the left,

10w = 200*5 + 300*2
10w = 1600
w = 160

Answer 2

A lever 9.000 m in length has the fulcrum placed at one end. A load of 26.000 kN is applied to a point 2.200 m from the fulcrum. What force must be applied to the end of the lever to place the system in equilibrium?

Answer 3

To find the load required at the extreme left end of the beam for equilibrium, we need to consider the forces acting on the beam.

Let's assume the left half of the beam (from the pivot point to the left end) as the first segment, and the right half (from the pivot point to the right end) as the second segment.

In order for the beam to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments. The moment of a force is the product of the force and the perpendicular distance from the pivot point (fulcrum).

Let's calculate the clockwise moments first:

Clockwise moment of the 200 Newton load:
Moment = Force × Distance
Clockwise moment = 200 N × 5 m

Clockwise moment of the 300 Newton load:
Moment = Force × Distance
Clockwise moment = 300 N × 8 m

Now, let's calculate the anticlockwise moments:

Anticlockwise moment of the load at the extreme left end (unknown):
Moment = Force × Distance
Anticlockwise moment = Load at extreme left end × 10 m (distance from the pivot point to the left end of the beam)

Since the beam is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

200 N × 5 m + 300 N × 8 m = Load at extreme left end × 10 m

Now we can solve the equation for the unknown load:

(200 N × 5 m + 300 N × 8 m) ÷ 10 m = Load at extreme left end

Calculating this equation:
(1000 + 2400) N ÷ 10 m = Load at extreme left end
3400 N ÷ 10 m = Load at extreme left end
Load at extreme left end = 340 N

Therefore, a load of 340 Newtons is required at the extreme left end of the beam for it to be in equilibrium.