A 0.5 kg ball is thrown horizontally towards a wall with a speed of 10 m/s. The initial velocity is chosen to be the positive x-direction for this question. The ball horizontally rebounds back from the wall with a speed of 10 m/s in the negative x-direction. What is momentum of the ball before it hits the wall, pi? What is momentum of the ball after it hits the wall, pf? What is the change in momentum of the ball, Δp? (Give both magnitude and direction for each answer.) Is momentum conserved for the ball?
isn't the change in momentum: Pf-Pi?
So wouldn't that mean:
-5-5=-10?
yeah i kno how to calculate those 2. i got 5 and -5...
so is momentum conserved?
because change in momentum would be
5 - (-5) = 10
but some ppl are telling me momentum is conserved because they are the same values.
what's the magnitude and direction?
To find the momentum of an object, we can use the formula:
momentum (p) = mass (m) × velocity (v)
Given information:
Mass of the ball (m) = 0.5 kg
Initial velocity of the ball (v) = 10 m/s in the positive x-direction
First, let's find the initial momentum of the ball before it hits the wall, pi:
pi = m × vi
Substituting the values:
pi = 0.5 kg × 10 m/s
Calculating:
pi = 5 kg·m/s (in the positive x-direction)
Next, let's find the momentum of the ball after it hits the wall, pf:
Since the ball rebounds and moves in the negative x-direction with the same speed, the velocity (vf) will be -10 m/s.
pf = m × vf
Substituting the values:
pf = 0.5 kg × (-10 m/s)
Calculating:
pf = -5 kg·m/s (in the negative x-direction)
Now, let's find the change in momentum of the ball, Δp:
Δp = pf - pi
Substituting the values:
Δp = (-5 kg·m/s) - (5 kg·m/s)
Calculating:
Δp = -10 kg·m/s
The magnitude of the change in momentum is 10 kg·m/s, and its direction is negative (in the x-direction).
Finally, let's analyze whether momentum is conserved for the ball:
Momentum is conserved when the total momentum before an event is equal to the total momentum after the event.
In this case, the total momentum before the ball hits the wall is pi = 5 kg·m/s in the positive x-direction.
The total momentum after the ball rebounds is pf = -5 kg·m/s in the negative x-direction.
Since the magnitudes and directions of the total momentum before and after the event are not equal, momentum is not conserved for the ball in this scenario.
The momentum of the ball is not conserved because of the force applied to it by the wall. You calculated the momentum change correctly. Ignore what "some people" say.
p is the symbol for momentum. pi means initial momentum and pf is the final momentum.
To calculate p, multiply mass M by velocity, V. They tell you what M and V are. The SIGN of V changes from + to - after the ball bounces.
Now, with that explanation, see if you can answer the questions by yourself.