Answer to Question #182205 in Mechanics | Relativity for Fatima Z

Question

A child weighs 15kg and slides with an initial speed of 1.5 m/s down a slide that is 4.0 m long as shown in the figure The slide makes a 40 angle with the horizontal. The child's speed at the bottom is 3.2 m/s i)What was the force of friction that the slide was exerting on the child?

ii) How much work did the friction do?

iii)How much work did gravity do? 

iv)How fast would the child travel if friction was negligible ?

v) What is the child's horizontal component of velocity?

Answer 1

$m\vec{g}+\vec{N}+\vec {F_{fr}}=m\vec a,$

$ma=mg\sin\alpha-\mu mg \cos\alpha,$

$\mu=\frac{g\sin\alpha-a}{g\cos\alpha},$

$a=\frac{v_2^2-v_1^2}{2l},$

1)

$F_{fr}=\mu N=\mu mg\cos\alpha=m(g\sin\alpha-\frac{v_2^2-v_1^2}{2l})=79.5~N,$

2)

$A_{fr}=F_{fr}l=318~J,$

3)

$A=mgh=mgl\sin\alpha=378~J,$

4)

$a'=g\sin\alpha=6.3~\frac{m}{s^2},$

$v_2'=\sqrt{v_1^2+2al}=7.3~\frac ms,$

5)

$v_{2x}=v_2\cos \alpha=(v_1+at)\cos\alpha=(1.15+0.76t)~\frac ms.$