## 1B 27

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Jamie Lee 1H
Posts: 54
Joined: Fri Aug 09, 2019 12:15 am

### 1B 27

A bowling ball of mass 8.00 kg is rolled down a bowling alley lane at 5.00 +/- 5.0 m/s. What is the minimum uncertainty in its position?
What value would you use as the change in uncertainty?

Jonathan Gong 2H
Posts: 105
Joined: Sat Jul 20, 2019 12:16 am

### Re: 1B 27

For minimum uncertainty, you would use 5.00 m/s as the velocity of the bowling ball.

Posts: 53
Joined: Thu Jul 25, 2019 12:17 am

### Re: 1B 27

1. By Heisenberg's Uncertainty Principle:
(uncertainty in momentum)(uncertainty in position) >/= (h)/(4 pi)

2. The given values in this problem allow you to calculate the uncertainty in momentum. Then, using Heisenberg's Uncertainty Principle, you must solve for the uncertainty in the position.

3. uncertainty in momentum = mass * (uncertainty in velocity) --> You are given that the mass of the bowling ball was 8.00 kg and that the actual speed of the ball was within 5 of 5 m/s. Thus, the uncertainty in velocity = 5 m/s
Now, you simply multiply the mass of the ball by uncertainty in velocity:
uncertainty in momentum = (8 kg) * (5 m/s) = 40 kg * m/s

4. Finally, plug in the uncertainty of momentum calculated in Step 3 into the equation for Heisenberg's Uncertainty Principle in Step 1 to find the uncertainty in the position. You should get (uncertainty in position) >/= 1.3 * 10 ^ -36 m. Since the problem asks for the minimum uncertainty in position, your answer is 1.3*10^-36 m.

Hope this helps!