Nitrogen gas molecules, which have mass 4.65×10−26 kg, are striking a vertical container wall at a horizontal velocity of positive 440 m/s. 5.00×1021 molecules strike the wall each second. Assume the collisions are perfectly elastic, so each particle rebounds off the wall in the opposite direction but at the same speed. (a) What is the change in momentum of each particle? (b) What is the average force of the particles on the wall?
I tried putting in the answers:
a)4.1e-23 kg*m/s
b)0.2 N
THESE WERE WRONG
Please help me :(
change of velocity = 880 m/s
change of momentum for each particle = 4092 * 10^-26 which is indeed 4.09*10^-23
*5*10^21 = 20*10^-2 = 2 *10^-1 Newtons
I agree with you
To solve this problem, we can use the equation for momentum:
Momentum = Mass * Velocity
Given that the mass of the nitrogen gas molecule is 4.65 × 10^-26 kg and the velocity is 440 m/s, we can calculate the momentum of each particle.
(a) Change in momentum of each particle:
Momentum before collision = Mass * Initial velocity
Momentum after collision = Mass * (-Initial velocity) [As the molecule rebounds in the opposite direction but at the same speed]
Change in momentum = Momentum after collision - Momentum before collision
= Mass * (-Initial velocity) - Mass * Initial velocity
= Mass * (-2 * Initial velocity)
Substituting the given values,
Change in momentum = (4.65 × 10^-26 kg) * (-2 * 440 m/s)
= -4.092 × 10^-23 kg·m/s
≈ -4.09 × 10^-23 kg·m/s
Therefore, the change in momentum of each particle is approximately -4.09 × 10^-23 kg·m/s.
(b) Average force of the particles on the wall:
The force exerted by each particle can be calculated using the formula:
Force = Change in momentum / Time interval
Given that 5.00 × 10^21 molecules strike the wall each second, the time interval between each collision is 1 second.
Substituting the values,
Force = (-4.09 × 10^-23 kg·m/s) / (5.00 × 10^21)
≈ -8.18 × 10^-44 N
Notice that the force is negative because the force exerted by each particle is in the opposite direction to the motion.
Therefore, the average force of the particles on the wall is approximately -8.18 × 10^-44 N.
Make sure to double-check your calculations to ensure accuracy.
To solve this problem, we can use the principles of Newton's laws of motion and the definition of momentum.
(a) To find the change in momentum of each particle, we can use the equation:
Change in momentum = Final momentum - Initial momentum
The final momentum of each particle can be calculated by multiplying the mass of the particle by its final velocity, which in this case is -440 m/s (since the particle rebounds off in the opposite direction):
Final momentum = mass * final velocity
= 4.65 × 10^(-26) kg * (-440 m/s)
Similarly, the initial momentum can be calculated by multiplying the mass of the particle by its initial velocity, which is 440 m/s:
Initial momentum = mass * initial velocity
= 4.65 × 10^(-26) kg * 440 m/s
The change in momentum of each particle is then given by the difference between the final and initial momentum.
(b) To calculate the average force of the particles on the wall, we can use the equation:
Average force = Change in momentum / Time
The change in momentum can be calculated using the formula from part (a), and the time per collision is the reciprocal of the number of collisions per second.
Average force = (4.65 × 10^(-26) kg * (-440 m/s)) / (1 / 5.00 × 10^21 s^(-1))
Now let's plug in the given values and solve the equations:
(a) Change in momentum:
Final momentum = -4.65 × 10^(-26) kg * 440 m/s = -2.046 × 10^(-23) kg·m/s
Initial momentum = 4.65 × 10^(-26) kg * 440 m/s = 2.046 × 10^(-23) kg·m/s
Change in momentum = -2.046 × 10^(-23) kg·m/s - 2.046 × 10^(-23) kg·m/s = -4.092 × 10^(-23) kg·m/s
(b) Average force:
Average force = (-4.092 × 10^(-23) kg·m/s) / (1 / 5.00 × 10^21 s^(-1))
= -2.046 × 10^(-2) N
After calculating, the correct answers are:
(a) The change in momentum of each particle is -4.092 × 10^(-23) kg·m/s.
(b) The average force of the particles on the wall is -2.046 × 10^(-2) N.
It's important to note that the negative sign in the answers indicates that the force and momentum are in the opposite direction of the initial velocity.