Equilibrium of the bodies on a inclined plane – application of the Newton’s first law problems and solutions

1. A 2-kg block lies on a rough inclined plane at an angle 37^o to the horizontal. Determine the magnitude of the external force exerted on the block, so the block is not slides down the plane. (sin 37^o = 0.6، کاز 37^o = 0.8، g = 10 ms ثانیې^-2، μ_k = 0.2)

پیژندل شوی:

ډله (m) = 2 kg

سرعت د جاذبې له امله (g) = ۱۰ متره/ ثانیه²

Block’s د وزن (w) = m g = (2)(10) = 20 Newton

ګناه ۳۷^o = 0.6

کاس 37^o = 0.8

Coefficient of the حرکي رګونه (µ_k) = 0.2،XNUMX

The y-component of the weight (w_y) = د کاس ایکس اینوم ایکس^o = (۱۹.۶)(۰.۵) = ۹.۸ نیوټن

The x-component of the weight (w_x) = w sin θ = (20)(sin 37) = (20)(0.6) = 12 Newton

the normal force (N) = w_y = ۱۰ نیوټن

پراري : The external force (F)

د حل :

w_x = ۱۰ نیوټن

The force of the kinetic friction (f_k) = μ_k N = (0.1)(16) = 1.6 Newton

The magnitude of the external force F exerted on the block :

ف + ف_k - w_x = 0

ف = w_x - f_k

F = 12 – 1.6

F = 10.4 نیوټن

The external force F greater than 10.4 Newton.

2. Mass of a block = 2 kg, coefficient of static friction µ_s = 0.4 and θ = 45^o. Determine the magnitude of the force F so the block start to slides up.

پیژندل شوی:

The coefficient of the static friction (µ_s) = 0.4،XNUMX

زاویه (θ) = 45^o

د جاذبې قوې له امله سرعت (g) = 10 m/s²

Block’s mass (m) = 2 kilogram

Block’s weight (w) = m g = (2 kg)(10 m/s²) = ۱۰ کیلوګرامه متر مکعب/ثانیه² = ۱۰ نیوټن

The x-component of the weight (w_x) = w sin θ = (20)(sin 45) = (20)(0.5√2) = 10√2 Newton

The y-component of the weight (w_y) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newton

پراري : The magnitude of the force F

حل:

Block starts to slide up, if F ≥ w_x + f_s.

The x-component of the weight :

w_x = ۹.۸√۳ نیوټن

the y-component of the weight :

w_y = ۹.۸√۳ نیوټن

نورمال ځواک :

ن = w_y = ۹.۸√۳ نیوټن

The force of the static friction :

f_s = μ_s ن = (۰.۵)(۴۰√۲) = ۲۰√۲

The magnitude of the force F so that the block starts to slide up :

F ≥ w_x + f_s

F ≥ ۴۰√۲ + 4√2

F ≥ 14√2 نیوټن

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1. Particles in one-dimensional equilibrium
2. Particles in two-dimensional equilibrium
3. Equilibrium of bodies connected by cord and pulley
4. Equilibrium of bodies on the inclined plane