PHYSICS - STATICS NEED detailed work please! thanks?

Question

1. A wooden beam 2 meters long with a mass of 5 kg is supported on two scales, one at the left end and the other one-half meter from the right end. A 10 kg weight is placed on the beam 0.2 m from the left end. What does the left side scale read? 

a) 98 N b) 73 N c) 49 N d) 36 N e) 25 N 

4. A 100 kg sofa 3 m long is carried by James and Sarah. James has the end, Sarah is holding the sofa 0.5 m from the other end. Some moron places a 50 kg box of books on the sofa on the very end of the sofa Sarah is holding. How much weight is Sarah holding now? 

a) 290 N b) 870 N c) 1180 N d) 1310 N e) 1470 N 

5. A 6 m long 20 kg ladder leans against a frictionless wall at an angle of 60o. What is the minimum coefficient of friction between the ladder and the floor? 

a) 0.1 b) 0.2 c) 0.3 d) 0.4 e) 0.5

 

 

Answer 1

(1)

Length of Wooden beam l = 2 m

Mass of Wooden beam m = 5 kg

Consider balance point b = l/2

b = 2/2 = 1 m

l₁ = l₂ = 1 m

At balancing point mass also shared as

m₁ = m₂ = 5 /2 = 2.5 kg

Additional 10 kg weight on the Wooden beam is placed at the left end.

So left side effective length and mass values will be changed.

m₁ = 2.5 + 10 = 12.5 kg

l₁ = 1 - 0.2 = 0.8 m

Wooden beam weight on left side for full length left side  w_{1 =} m₁g

w₁ = 12.5*9.8 = 122.5

But wooden beam is placed at 0.2 m from the left end.

w₁ = 122.5*0.8 = 98 N

The left side scale reading is 98N

Answer is Option(a)

Answer 2

(4)

Length of sofa l = 3 m

Mass of sofa m = 100 kg

Consider balance point b = l/2

b = 3/2 = 1.5 m

l₁ = l₂ = 1.5 m

At balancing point mass also shared as

m₁ = m₂ = 5 /2 = 2.5 kg        

Additional box of 50 kg mass on the sofa is placed at the end which sarah is holding.

So left side effective length and mass values will be changed.

m₁ = 100 + 50 = 150 kg

Sofa weight on sarah holding side for full length w_{1 =} m₁g

w₁ = 150*9.8 = 1470

But Sarah is holding the sofa 0.5 m from the other end

Effective length l₁ = 1.5 - 0.5 = 1 m

w₁ = 1470*1 = 1470 N

The weight Sarah holding now is 1470 N

Answer is Option(e)