Momentum Conservation: Bullet enters a block

AI Thread Summary
The discussion centers on the application of conservation of momentum in a scenario involving a bullet entering a block. The initial confusion arises from the need to determine the variable V, which is dependent on height h. A participant clarifies that the equation involving l, h, and a is derived from Pythagoras' theorem. By expanding the equation and simplifying, the relationship becomes clearer. The explanation ultimately resolves the confusion regarding the variables involved.
Shreya
Messages
187
Reaction score
64
Homework Statement
I am not able to solve the second part of the question.
Please refer the image below.
V refers to the final velocity after collision, v is the initial velocity of bullet. L is the length of string and h is the height that the block rises to.
Relevant Equations
Conservation of Momentum
I can understand that using conservation of momentum, we can find v. But we need V for that. The equation for V involves h and so we need h. But I am not able to comprehend the equation involving l,h and a. The question doesn't specify what a is.
Please be kind to help
 

Attachments

  • Screenshot_20220328-092428_Drive.png
    Screenshot_20220328-092428_Drive.png
    23.7 KB · Views: 141
  • Screenshot_20220328-092536_Drive.png
    Screenshot_20220328-092536_Drive.png
    22.8 KB · Views: 146
Physics news on Phys.org
That’s just Pythagoras’ theorem.
$$
l^2 = (l-h)^2 + a^2
$$
Expand the (l-h) square and cancel ##l^2## on both sides.
 
Last edited:
  • Like
Likes Delta2 and Shreya
Orodruin said:
That’s just Pythagoras’ theorem.
Thanks @Orodruin! I get it now.
 
Last edited:
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top