Question

Please solve 3 A and B & just leave it in terms of variables

Neglect air resistance. Consider the arrow shot at a pendulum, consisting of a mass m, suspended by a non-stretch string, as shown in the figures below. 3. Vo,mo Vo,mo How high will the block in figure (a) rise if the arrow embeds within it? Will the block in figure (b) rise to a greater or lower height than the one in (a)? The values of wou moy h, and m, are the same as in figure (a), but the steepness of the trajectory is different. a. b.

Answer 1

a)

v_ox = horizontal component of velocity of arrow just before collision

V_o = intial velocity of hanging mass before collision

V = final velocity of arrow-block combination after collision

using conservation of momentum

m_o v_ox + m₁ V_o= (m_o + m₁) V

m_o v_ox + m₁ (0) = (m_o + m₁) V

V = m_o v_ox /(m_o + m₁)                                                      eq-1

h' = height gained by the combination after collision

using conservation of energy

(0.5) (m_o + m₁) V² = (m_o + m₁) g h'

(0.5) V² = g h'

(0.5) (m_o v_ox /(m_o + m₁) )² = g h'

h' = (m_o v_ox /(m_o + m₁) )² /(2g)

b)

in figure b, the horizontal component of velocity of arrow before collision is smaller . hence the speed of the combination after the collision also comes out to be smaller. Since the heioght gained depends on the speed after collision, hence the speed gained after collision becomes smaller