Need help using algebra to solve physics equations

In summary, the conversation involves solving for the final velocities of two balls after a collision, one elastic and one completely inelastic. The first equation is used to solve for the final velocity of the first ball, and the second equation is used to solve for the final velocity of the second ball. The conversation includes a step-by-step explanation of how to use algebra to solve for the final velocity of the second ball. The final velocities obtained are -0.4 m/s and 1.6 m/s.
  • #1
My question is not so much what to do it is just i have problems solving for a certain equation.

A 5.00kg ball, moving to the right at a velocity of 2m/s on a frictionless table, collides head-on with a stationary 7.50kg ball. Find the final velocities of the balls if the collision is (a) elastic and (b) completely inelastic

for part A

I have m1v1f + m2v2f= m1vi1 +0
to solve for final velocity 1(the ball for 5kg) you use

vf1=(m1-m2/m1+m2)vi1

I really have no i do how to algebraically solve for vf1, can someone explain that to me because when i use the equation i get the right answer which is -.400m/s

To find vf2 we use the fact that it is an ellastic collision and the kinetic energy before and after is the same

1/2m1(vf1^2)+1/2m2(vf2^2)=1/2m1(vi1^2)+0
Using this i have to solve for vf2 but again i have a problem algebraically solving for vf2. But there is a similar example in the textbook so i used what they had to solve for vf1 and vf2 but they do not show the work

vf2=(2m1/m1+m2)vi1
answer should be 1.60m/s

My problem is not understand ellastic equations, it is how to solve the first equation for vf1 and the second for vf2. Can someone show me step by step how to use algebra to solve for vf2 with what i typed above,
 
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  • #2
so i just did this in lab last week so I am able to help you...

1/2 m1(vi1^2) + 0 = 1/2m1(vf1^2) + 1/2 m2(vf2^2)

all the 1/2s cancel

m1(vi1^2) = m1(vf1^2) + m2(vf2^2)

momentum before = momentum after
m1(vi1) = m1(vf1) + m2(vf2) ---> vf1 = [m2(vf2) - m1(vi1)] / m1

plug vf1 solved above into equation

m1(vi1^2) = m1 ([m2vf2 - m1vi1] / m1)^2 + m2(vf2^2)

m1(vi1^2) = m1 [(m2vf2 - m1vi1)/m1][(m2vf2 - m1vi1)/m1] + m2(vf2^2)

m1(vi1^2)=m1/m2[m2^2(vf2^2) - 2m2vf2m1vi1 + m1^2(vi1^2)]+m2(vf2^2)

(m1/m2 = 1/m1 so multiply both sides by m1 to give the left side m1^2 and the right side m1m2(vf2^2) and everything else stays the same)

m1^2(vi1^2) =m2^2(vf2^2)-2m2vf2m1vi1 + m1^2(vi1^2) + m1m2(vf2^2)

the m1^2(vi1^2) on both sides cancel

0 = m2vf2(m2v2f - 2m1vi1 + m1vf2)

set m2v2f - 2m1vi1 + m1vf2 = 0
(please don't ask me why bc i didnt really understand bc my teacher just said well one of them must be equal to zero because the equation is equal to 0)

m2vf2 + m1vf2 = 2m1vi1

from here its easy to solve for vf2 then plug the solution into the momentum before = momentum after equation and solve for vf1

I had problems with the algebra for this too...i hate using variables and not numbers. I hope this helps and you can understand each step, its hard to type it all out. Good luck!
 
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  • #3
since yu have the masses sub for them in the 2 equations. you obtain
5 v1f + 7.5 v2f = 10 ...(1) and
(1/2) 5 v1f^2 + (1/2) 7.5 v2f^2 = (1/2) 20 ...(2)
now divide eq # (2) by (1/2) also
divide both eq by 5 to siplify - you get
v1f + 1.5 v2f = 2 ...(3) and
v1f^2 + 1.5 v2f^2 = 4 ...(4)
see how simple they became
solve # (3) for v1f and sub in # (4)
solve the quadratic you obtained from # (4)
you will get v2f
sub this value in # (3)
and here you go you obtain v1f
The answers I obtained for
v1f is - 0.4 m/s and for
v2f is 1.6 m/s
Best wishes.
 

1. What is the relationship between algebra and physics?

Algebra is a branch of mathematics that uses letters and symbols to represent quantities and their relationships. In physics, algebra is used to express physical laws and solve equations that represent real-world phenomena. It provides a powerful tool for understanding and predicting the behavior of physical systems.

2. How can I use algebra to solve physics equations?

To solve physics equations using algebra, you first need to identify the variables involved and their relationships. Then, you can use algebraic operations such as addition, subtraction, multiplication, and division to manipulate the equations and solve for the unknown variable. It is important to follow the correct order of operations and keep track of units to ensure accurate solutions.

3. Can algebra be used to solve any physics problem?

Algebra can be used to solve a wide range of physics problems, from simple motion equations to more complex systems involving multiple equations and variables. However, there may be cases where other mathematical methods, such as calculus, are better suited for solving certain physics problems. It is important to have a strong foundation in algebra to effectively apply it to physics problem-solving.

4. What are some common mistakes when using algebra to solve physics equations?

One common mistake is not paying attention to units. In physics, units must be consistent throughout the entire equation. Another mistake is not following the correct order of operations, which can lead to incorrect solutions. It is also important to double check your calculations and make sure you have correctly solved for the unknown variable.

5. How can I improve my algebra skills for solving physics equations?

Practice is key for improving your algebra skills for physics problem-solving. Start with simple equations and gradually work your way up to more complex ones. It is also helpful to understand the concepts and principles behind the equations, rather than just memorizing formulas. Seeking help from a tutor or using online resources can also aid in improving your algebra skills for solving physics equations.

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