1. A 2-kg block lies on a rough inclined plane at an angle 37o to the horizontal. Determine the magnitude of the external force exerted on the block, so the block is not slides down the plane. (sin 37o = 0.6, cos 37o = 0.8, g = 10 m.s-2, µk = 0.2)
Known :
Mass (m) = 2 kg
Acceleration due to gravity (g) = 10 m/s2
Block’s weight (w) = m g = (2)(10) = 20 Newton
Sin 37o = 0.6
Cos 37o = 0.8
Coefficient of the kinetic friction (µk) = 0.2
The y-component of the weight (wy) = w cos 37o = (20)(0.8) = 16 Newton
The x-component of the weight (wx) = w sin θ = (20)(sin 37) = (20)(0.6) = 12 Newton
the normal force (N) = wy = 16 Newton
Wanted : The external force (F)
Solution :
wx = 12 Newton
The force of the kinetic friction (fk) = µk N = (0.1)(16) = 1.6 Newton
The magnitude of the external force F exerted on the block :
F + fk – wx = 0
F = wx – fk
F = 12 – 1.6
F = 10.4 Newton
The external force F greater than 10.4 Newton.
2. Mass of a block = 2 kg, coefficient of static friction µs = 0.4 and θ = 45o. Determine the magnitude of the force F so the block start to slides up.
Known :
The coefficient of the static friction (µs) = 0.4
Angle (θ) = 45o
Acceleration due to gravity (g) = 10 m/s2
Block’s mass (m) = 2 kilogram
Block’s weight (w) = m g = (2 kg)(10 m/s2) = 20 kg m/s2 = 20 Newton
The x-component of the weight (wx) = w sin θ = (20)(sin 45) = (20)(0.5√2) = 10√2 Newton
The y-component of the weight (wy) = w cos θ = (20)(cos 45) = (20)(0.5√2) = 10√2 Newton
Wanted : The magnitude of the force F
Solution :
Block starts to slide up, if F ≥ wx + fs.
The x-component of the weight :
wx = 10√2 Newton
the y-component of the weight :
wy = 10√2 Newton
The normal force :
N = wy = 10√2 Newton
The force of the static friction :
fs = µs N = (0,4)(10√2) = 4√2
The magnitude of the force F so that the block starts to slide up :
F ≥ wx + fs
F ≥ 10√2 + 4√2
F ≥ 14√2 Newton
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- Particles in one-dimensional equilibrium
- Particles in two-dimensional equilibrium
- Equilibrium of bodies connected by cord and pulley
- Equilibrium of bodies on the inclined plane