Two people sitting on rolling chairs with little friction push off from each other so that they move apart. On is 60 kg and one is 40 kg. If the 40 kg person recoils at 4.3 m/s, what will the veloocity of the 60 kg person's recoil in m/s
mivi=mfvf
40v...how do I get v with m and t?
First off, always do a sanity check when you get your answer.
The two people were roughly the same mass, so their velocities should be roughly the same. Your answer was clearly unreasonable.
conserve momentum. Since everything was initially at rest, we need
m1v1 + m2v2 = 0
40 * 4.3 + 60 v2 = 0
v2 = -2.87 m/s
or is it 4.3 m/s=-60v
v=-.071??
I was reading the problem that the 40kg recoiled in 4.3 seconds.
I'm tired :(
Well, first of all, we need to use some physics equations here. Specifically, we'll be using the principle of conservation of momentum.
Now, the principle of conservation of momentum states that the total momentum of an isolated system remains constant unless acted upon by an external force. In this case, the system consists of the two people on rolling chairs.
So, let's calculate the initial momentum of the system:
Initial momentum = (mass1 * velocity1) + (mass2 * velocity2)
Here, mass1 is 60 kg and mass2 is 40 kg.
As per the question, the 40 kg person recoils at a speed of 4.3 m/s. So, we can replace the values in the equation:
Initial momentum = (60 kg * velocity1) + (40 kg * 4.3 m/s)
Now, since the two people are pushing off from each other, their total momentum remains constant but with opposite signs.
Therefore, the equation becomes:
(60 kg * velocity1) + (40 kg * 4.3 m/s) = 0
Now, we can solve for velocity1:
60 kg * velocity1 = - (40 kg * 4.3 m/s)
velocity1 = - (40 kg * 4.3 m/s) / 60 kg
Calculating that, we find that velocity1 is approximately -2.87 m/s.
So, the velocity of the 60 kg person's recoil is approximately -2.87 m/s. Keep in mind that the negative sign indicates the direction of the motion.
Remember, no need to worry about the negative sign; it's just a sign that humorously indicates you've moved away from each other!
To solve for the velocity of the 60 kg person's recoil (vf), you can use the law of conservation of momentum. According to this law, the total momentum before the push must be equal to the total momentum after the push.
The momentum of an object is calculated by multiplying its mass (m) by its velocity (v). In this case, the momentum of the 40 kg person before the push is given as:
p1 = m1 * v1, where m1 = 40 kg and v1 = 4.3 m/s.
Now, let's assign the velocity of the 60 kg person before the push as v2. The momentum of the 60 kg person before the push is:
p2 = m2 * v2, where m2 = 60 kg and v2 = ?
Since the two people are pushing off from each other, the direction of the velocity for one person will be opposite to the other. This means that the magnitude of the velocity of the 60 kg person, v2, will be the same as that of the 40 kg person, v1, but with an opposite sign.
Using the conservation of momentum, we can now set up the equation:
p1 + p2 = 0
(m1 * v1) + (m2 * v2) = 0
Substituting the known values:
(40 kg * 4.3 m/s) + (60 kg * v2) = 0
Simplifying the equation:
172 kg·m/s + 60 kg·v2 = 0
60 kg·v2 = -172 kg·m/s
Dividing both sides by 60 kg:
v2 = -172 kg·m/s / 60 kg
v2 ≈ -2.87 m/s
Therefore, the velocity of the 60 kg person's recoil is approximately -2.87 m/s. Note that the negative sign indicates that the person is moving in the opposite direction to the 40 kg person's recoil.