Answer:
a) W = 6.75 J and b) v = 3.87 m / s
Explanation:
a) In the problem the force is nonlinear and they ask us for work, so we must use it's definition
W = ∫ F. dx
Bold indicates vectors. In a spring the force is applied in the direction of movement, whereby the scalar product is reduced to the ordinary product
W = ∫ F dx
We replace and integrate
W = ∫ (-60 x - 18 x²) dx
W = -60 x²/2 -18 x³/3
Let's evaluate between the integration limits, lower W = 0 for x = -0.50 m, to the upper limit W = W for x = 0 m
W = -30 [0- (-0.50) 2] -6 [0 - (- 0.50) 3]
W = 7.5 - 0.75
W = 6.75 J
b) Work is equal to the variation of kinetic energy
W = ΔK
W = ΔK = ½ m v² -0
v =√ 2W/m
v = √(2 6.75/ 0.90)
v = 3.87 m / s
Answer:
Explanation:18kt alloy contains
i) 75% of gold
rhogold=19.3g/cm^3
=75/100×19.3
=14.475g/cm^3
ii) 16% of silver
rhosilver=10.5g/cm^3
=16/100×10.5
=1.68g/cm^3
iii) 9% of copper
rhocopper =8.90g/cm^3
=9/100×8.9
=0.801g/cm^3
Overall density of 18kt gold
=(0.801+1.68+14.475)g/cm^3
=16.956g/cm^3
=17g/cm^3 to 3s.f
According to the conservation of mechanical energy, the kinetic energy just before the ball strikes the ground is equal to the potential energy just before it fell.
Therefore, we can say KE = PE
We know that PE = m·g·h
Which means KE = m·g·h
We can solve for h:
h = KE / m·g
= 20 / (0.15 · 9.8)
= 13.6m
The correct answer is: the ball has fallen from a height of 13.6m.
