Question-69829

Question Number 69829 by TawaTawa last updated on 28/Sep/19

Commented by TawaTawa last updated on 28/Sep/19

The question says do not use {Newton}^{'} s law and kinematic

Commented by TawaTawa last updated on 28/Sep/19

Help with the (b) sir

Answered by mr W last updated on 28/Sep/19

(b)

e n e r g y a t t h e b e g i n n i n g :

E_{1} = \frac{1}{2} {m v}^{2}

e n e r g y a t t h e e n d :

E_{2} = m g h

w o r k d o n e b y t h e g r a v i t y f o r c e :

- m g h

f r i c t i o n f o r c e :

f = μ N = μ m g \cos θ

w o r k d o n e b y t h e f r i c t i o n f o r c e :

- f s = - f \frac{h}{\sin θ} = - \frac{μ m g h}{\tan θ}

w o r k = e n e r g y c h a n g e

- m g h - \frac{μ m g h}{\tan θ} = m g h - \frac{1}{2} {m v}^{2}

\Rightarrow μ = (2 - \frac{v^{2}}{2 g h}) \tan θ = (2 - \frac{12^{2}}{2 \times 10 \times 5}) \times \tan 45 ° = 0.56

Commented by TawaTawa last updated on 28/Sep/19

God bless you sir

Answered by mr W last updated on 28/Sep/19

(a)

w o r k d o n e b y t h e p u l l i n g f o r c e :

F \cos θ s = 20 \times \frac{4}{5} \times 5 = 80 J

f r i c t i o n f o r c e :

f = μ N = μ (m g - F \sin θ) = 0.1 (10 \times 10 - 20 \times \frac{3}{5}) = 8.8 N

w o r k d o n e b y t h e f r i c t i o n f o r c e :

f s = - 8.8 \times 5 = - 44 J

w o r k d o n e b y a l l f o r c e s :

W = 80 - 44 = 36 J

k i n e t i c e n e r g y o f m a s s :

E = \frac{1}{2} {m v}^{2}

w o r k = e n e r g y c h a n g e :

W = E

36 = \frac{1}{2} \times 10 \times v^{2}

\Rightarrow v = \sqrt{\frac{36}{5}} = \sqrt{7.2} = 2.68 m / s

Commented by TawaTawa last updated on 28/Sep/19

Wow, God bless you sir . I appreciate your time