Question

When a force of 50 N is applied on a body of mass 10 kg it is about to move and once the body is set
into motion the same force of 50 N produces an acceleration of 0.5 m/s Find coefficient of static and
kinetic friction (g = 10 m/s)
1) 0.4.0.49
2) 0.5, 0.49 3) 0.5, 0.6
4) 0.4.0.4​

Answer 1

Answer :-

$\mu_s = 0.5$

$\mu_k = 0.45$

Given :-

m = 10 kg

F = 50 N

a = 0.5 m/s²

To find :-

The coefficient of static and kinetic friction.

Solution:-

Let $\mu_s$ and $\mu_k$ be the static friction coefficient and kinetic friction coefficient respectively.

• Since, This is the case of Limiting equilibrium.

Therfore,

→$F - f_s = ma$(a = 0)

→$F = f_s$

→$F = \mu_s mg$

→$50 = \mu_s 10 \times 10$

→$50 = 100 \mu_s$

→$\mu_s = \dfrac{50}{100}$

→$\mu_s = 0.5$

hence,

The static friction coefficient is 0.5.

Now ,

Body has some acceleration

→$F - f_k = ma$

→$F -\mu_k mg = ma$

→$50 - \mu_k 10 \times 10 = 10 \times \dfrac{5}{10}$

→$50 - \mu_k100= 5$

→$50 -5 = 100 \mu_k$

→$45 = 100\mu_k$

→$\mu_k = \dfrac{45}{100}$

→$\mu_k = 0.45$

hence,

The coefficient of kinetic friction is 0.45.