Question

A uniform plank of weight 100 N is 2000 mm long and rests on a support that is 400 mm from end E. At what distance from E must a 160 N weight be placed in order to balance the plank?

Answer 1

Answer:

the location of 160 N from end E is 25mm

Explanation:

given:

A uniform plank of weight 100 N is 2000 mm long

and rests on a support that is 400 mm from end E

find:

At what distance from E must a 160 N weight be placed in order to balance the plank?

                                                                      160 N

                                                                           |---x--->|

                                      100N                           \|/

======================||======================E

                                                            Δ---- 400mm---->|

|<----------------------------  2000mm   --------------------------->|

to determine the location of 160N load in order to balance the plank,

you have to take moment at support Δ.

note:

the 100 N is located at the center of a plank.

the distance of 100N from support = (2000 / 2) - 400 = 600mm

∑moment at Δ = 0

0 = -100 N (600mm) + 160 N (400-x)

0 = -60000 N.mm + 64000 N.mm - 160x N.mm

0 = 4000 - 160x

160x = 4000

x = 4000/160

x = 25 mm

therefore,

the location of 160 N from end E is 25mm