Anonymous
Anonymous asked in Science & MathematicsZoology · 3 weeks ago

A sandbag is mounted on a cart that is at rest on a frictionless surface, and their total mass is 4.5 kg. What will be the velocity of the cart and sandbag if a bullet of a mass of 2.0 g is fired into the sandbag with a horizontal velocity of 500 m/s?

Relevance
• 3 weeks ago

4.5 kg = 4500 g

m1 * v1 + m2 * v2 = m3 * v3

m3 = m1 + m2 = 4500 + 2 = 4502 grams

4500 * 0 + 2 * 500 = 4502 * v

1000 = 4502 * v

1000 / 4502 = v

v = ‭0.22212350066637050199911150599733‬...

0.222 m/s

• Andrew Smith
Lv 7
3 weeks agoReport

One thing you should consider.  Both "4.5" and "2.0" contained only 2 significant figures so even 0.222 is claiming more accuracy than the question permitted.

• oubaas
Lv 7
3 weeks ago

Momentum shall be conserved, therefore :

V = (mb*Vb)/(mb+mc) = 2*500/(1000*4.502) = 1/4.502 m/sec ( 0.2221... )

lost energy LE = (5^2*10^4*10^-3)-4.502/2*(1/4.502)^2 = 250-0.11 = 249.9 joule

• 3 weeks ago

Since momentum is conserved, and it is an inelastic collision since they stick together;

m1v1 + m2v2 = (m1 + m2)v3, where v3 is the final velocity of the cart and sandbag

v2 = 0 since the cart is at rest, and m2 = 0.002 kg, therefore

v3 = (m1v1)/(m1+m2) = 0.222m/s

• 3 weeks ago

Why would someone put a sandbag in a cart? That's just crazy.