Question

If the coefficient of friction between all surfaces
is 0.5, then find the minimum force F to have
equilibrium of system. (assume strings and
pulleys are massless)
Critical
Thinking
4000
-N
17
(a)
1000
T
N
O
Mac
17
(
b) (c
)
Т.
T3
2000
$0 kg
N
500 kg
F
17
500
-N
17
(d)​

Answer 1

Correct question:

If the coefficient of friction between all surfaces is 0.5, then find the minimum force F to have an equilibrium of the system. (Assume strings and pulleys are massless)

a) 1000N

b) 200N

c) 500N

d) 50N

Answer:

The minimum force F required is 50N.

Explanation:

Using the given figure

For 15kg block,

N = F

μN + T = m₁g

T = m₁g - μF ...(i)

For 25kg block,

N' = F

m₂g = μF + 2T - μF

m₂g = 2T ...(ii)

From (i) and (ii), we get

m₂g = 2(m₁g - μF)

m₂g  - 2m₁g = -2μF

F = (m₂g  - 2m₁g)/ -2μ

F = g(2m₁ - m₂)/2μ

Substituting the given values, we get

F = 10(2×15 - 25)/2×0.5

F = 10(30-25)/1

F = 10(5)

F = 50N

Therefore, the minimum force required to have an equilibrium of the system is 50N.

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