Help with Linear momentum problem

In summary, when two particles with masses mA = 9.11x10^31 kg and mB = 1.67x10^-27 kg are released from rest with a distance between them of Di = 3.0x10^-6 m, and then their distance is decreased to D = 1.0x10^-6 m, the ratio of their linear momentums, speeds, and kinetic energies can be found by using the conservation of momentum principle and the given initial conditions.
  • #1
missrikku
Hello again!

I am having trouble with the following linear momentum problem:

A has a mass mA = 9.11x10^31 kg
B has a mass mB = 1.67x10^-27 kg

They are attracted to each other by some electrical force.

Say they are released from rest with a distance between them of Di = 3.0x10^-6 m

When their distance is decreased to D = 1.0x10^-6 m, what is the ratio of

a) their linear momentums

b) speeds

c) kinetic energies

-----

i know:

p = mv

so for a)

I am looking for: Pe/Pp
mAvA/mBvB

I have mA and mB, but not vA or vB

I know that they are released from rest, but how do you find vA and vB?

Can I use V^2 = Vi^2 + 2a(D-Di) ? If so, how do I find the a?

Thanks. I just need to be pointed in the right direction.
 
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  • #2
Actually, the phrasing of the questions is a major hint. Notice that the question does not ask for the momenta or velocities of the separate particles but only for the ratios. Also the problem asks first for the ratio of the momenta- if you find that first, the others are easy.
Since the force attracting the two particles to one another is "internal", momentum is conserved- that is, MAvA+ MBvB is a constant.. Since the two particles were initially motionless, what was the initial momentum of each and what was the total momentum (the "constant")?
 
  • #3


Hi there,

To solve this problem, we can use the conservation of momentum principle, which states that the total momentum of a closed system remains constant. In this case, the system is closed since there are no external forces acting on A and B.

a) To find the ratio of their linear momentums, we can use the equation p = mv. Since they are released from rest, their initial momentums are both zero. When their distance is decreased to D = 1.0x10^-6 m, their final momentums can be calculated using the equation p = mv again. So the ratio of their momentums will simply be the ratio of their masses, since their velocities are the same. Therefore, Pe/Pp = mA/mB = 9.11x10^31/ 1.67x10^-27 = 5.46x10^58.

b) To find the ratio of their speeds, we can use the equation v = sqrt(2K/m), where K is the kinetic energy and m is the mass. Since the initial kinetic energy is zero, we can only calculate the final kinetic energy using the equation K = (1/2)mv^2. Plugging in the values, we get K = (1/2)(1.67x10^-27)(v^2). To find the speed, we can rearrange the equation to v = sqrt(2K/m). So the ratio of their speeds will be vA/vB = sqrt(mB/mA) = sqrt(1.67x10^-27/9.11x10^31) = 1.38x10^-16.

c) Finally, to find the ratio of their kinetic energies, we can use the equation K = (1/2)mv^2. We already have the values for m and v from the previous calculations, so we can plug them in to get the kinetic energies for A and B. The ratio of their kinetic energies will be Kp/Ke = (1/2)mA*vA^2/(1/2)mB*vB^2 = (mA*vA^2)/(mB*vB^2) = (mA/mB)*(vA/vB)^2 = 9.11x10^31/1.67x10^-27 * (1.38x10^-16)^2 = 2.84x10^34.

I hope
 

1. What is linear momentum?

Linear momentum is a measure of an object's motion, specifically its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. It is often referred to as the "quantity of motion" of an object.

2. How do I calculate linear momentum?

Linear momentum is calculated by multiplying an object's mass by its velocity. The formula is: p = m x v, where p is linear momentum, m is mass, and v is velocity. The standard unit for linear momentum is kilogram-meters per second (kg*m/s).

3. What is the principle of conservation of linear momentum?

The principle of conservation of linear momentum states that the total linear momentum of a system remains constant unless acted upon by an external force. This means that in a closed system, the initial linear momentum of all objects will be equal to the final linear momentum.

4. How is linear momentum related to Newton's laws of motion?

Newton's second law of motion states that the net force acting on an object is equal to its mass multiplied by its acceleration. This can also be written as F = m x a. By rearranging this equation, we can see that m x a = p/t, or mass times acceleration is equal to change in linear momentum over time.

5. Can you provide an example of a linear momentum problem?

Sure! Let's say a 5 kg ball is traveling at a velocity of 10 m/s to the east. What is its linear momentum? Using the formula p = m x v, we can calculate that the ball's linear momentum is 50 kg*m/s to the east. If the ball collides with another ball of equal mass traveling at the same velocity in the opposite direction, what is the final velocity of the two balls? The total initial linear momentum is 100 kg*m/s to the east (50 kg*m/s + (-50 kg*m/s)). As the linear momentum must be conserved, the final total linear momentum must also be 100 kg*m/s. Therefore, the final velocity of the two balls will be 10 m/s to the east.

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