Answer to Question #105803 in Classical Mechanics for Billy

Question

i got 2 questions. One motions one Newton’s Law

Q1) Object A is dropped from height h.At the same instant object B is thrown vertically upwards from the ground. Right before they collide in mid-air, the speed of A is twice of the speed of B. Determine the height h of collision

Q2) The pages of 2 identical books A and B are overlapping on one and another. The mass of each book is 1000g and the number of pages is \mu =0.3 . Book A is fixed on the table which a horizontal force F is pulling book B. Determine the minimum value of F to pull book B out.

Answer 1

1)

For the object A

applying formula $v^2=u^2+2gS$

$v^2=0+2\times g\times h/2 \\v=\sqrt{gh}$

For the object B , speed at mid height

applying formula $v^2=u^2+2(-g)S$

$v^2=v_b^2-2\times g\times h/2\\v=\sqrt{v_b^2-gh}$

it is given that the speed of A is twice of the speed of B

$\sqrt{gh}=2\sqrt{v_b^2-gh}$

$gh=4(v_b^2-gh)\\5gh=4v_b^2\\h=\dfrac{4v_b^2}{5g}$

2) Normal force = mg=10N

maximum frictional force = $\mu$N =0.3x10=3N

so the minimum force needed to pull the book B is 3N