Question

1. A force acts on a 2 kg mass and gives it an acceleration of 3 m/s2. What acceleration is produced by the same force when acting on a mass of:

a) 1 kg (ans = 6)

2. A horizontal force of 200 N is required to cause a 15 kg block to slide up a 20 degree incline with an acceleration of 0.25 m/s2. Find:

a) the friction force on the block (ans = 134 N)

b) the coefficient of friction (0.65)

Answer 1

Question 1

Mass of the first object = m₁ = 2 kg

Acceleration of the first object due to the force = a₁ = 3 m/s²

Force acting = F

F = m₁a₁

F = (2)(3)

F = 6 N

Mass of the second object = m₂ = 1 kg

Acceleration of the second object due to the force = a₂

F = m₂a₂

6 = (1)a₂

a₂ = 6 m/s²

Acceleration produced when the same force acts on a 1 kg mass = 6 m/s²

Question 2

Free Body Diagram N a mysinot m fluo f TL Fsine mglos o

Gravitational acceleration = g = 9.81 m/s²

Mass of the block = m = 15 kg

Horizontal force on the block = F = 200 N

Angle of the incline = $\theta$ = 20^o

Acceleration of the block = a = 0.25 m/s²

Normal force on the block from the incline = N

Friction force on the block from the incline = f

From the free body diagram,

N = mgCos$\theta$ + FSin$\theta$

N = (15)(9.81)Cos(20) + (200)Sin(20)

N = 206.7 N

ma = FCos$\theta$ - mgSin$\theta$ - f

(15)(0.25) = (200)Cos(20) - (15)(9.81)Sin(20) - f

f = 134 N

Coefficient of friction = $\mu$

f = $\mu$ N

134 = $\mu$ (206.7)

$\mu$ = 0.65

a) Friction force on the block = 134 N

b) Coefficient of friction = 0.65