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Maru [420]
3 years ago
15

The muzzle velocity of a rifle bullet is 709 m s−1along the direction of motion. If the bullet weighs 35 g, and the uncertainty

in its momentum is 0.20%, how accurately can the position of the bullet be measured along the direction of motion?
Physics
1 answer:
nydimaria [60]3 years ago
7 0

Answer:

Uncertainty in position of the bullet is \Delta x=1.07\times 10^{-33}\ m

Explanation:

It is given that,

Mass of the bullet, m = 35 g = 0.035 kg

Velocity of bullet, v = 709 m/s

The uncertainty in momentum is 0.20%. The momentum of the bullet is given by :

p=mv

p=0.035\times 709=24.81\ kg-m/s

Uncertainty in momentum is,

\Delta p=0.2\%\ of\ 24.81

\Delta p=0.049

We need to find the uncertainty in position. It can be calculated using Heisenberg uncertainty principal as :

\Delta p.\Delta x\geq \dfrac{h}{4\pi}

\Delta x=\dfrac{h}{4\pi \Delta p}

\Delta x=\dfrac{6.62\times 10^{-34}}{4\pi \times 0.049}

\Delta x=1.07\times 10^{-33}\ m

Hence, this is the required solution.

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An object with total mass mtotal = 14.6 kg is sitting at rest when it explodes into three pieces. One piece with mass m1 = 4.9 k
zheka24 [161]

Answer: 1) 0. 2) 4.2 Kg. 3) 15.4 m/s 4) 12.9 m/s 5) 0. 6) 3.62 KJ.

Explanation:

1) Assuming that no external forces act during the collision, total momentum must be conserved. As initially the total mass was at rest, so initial momentum is zero, final momentum of all the system must be 0 also.

2) After the explosion, as mass must be conserved also, the sum of the masses of the three pieces must be equal to the original total mass, so we can write the following:

m₁ + m₂ + m₃ = M = 14.6 Kg = 4.9 Kg + 5.5 Kg + m₃

Solving for m₃, we have:

m₃ = 14.6 Kg - 4.9 Kg -5.5 Kg = 4.2 Kg.

3) and 4)

As momentum is a vector, if it is magnitude must be 0, this means that all his components must be 0 too.

So, we can write two equations, one for the x-component, and other for the y-component, as follows:

pₓ = m₁. v₁ₓ + m₂.v₂ₓ + m₃.v₃ₓ = 0

py = m₁.v₁y + m₂. v₂y + m₃. v₃y =0

Replacing by the values, and solving for v₃ₓ and v₃y, we get:

v₃ₓ = 15.4 m/s

v₃y = 12.9 m/s

v = √(15.4)²+(12.9)² = 20.1 m/s

5) As the center of mass must move as if all the mass were concentrated in this point, and we know that the total momentum must be 0, this tells us that the magnitude of the velocity of the center of mass must be 0 too.

6) As initial kinetic energy is 0, as  the mass was at rest, the increase in the kinetic energy is obtained simply adding the kinetic energy of every piece of mass gained after explosion, as follows:

K = K₁ + K₂ + K₃ = 1/2 (m₁ . v₁² + m₂.v₂² + m₃.v₃²)

Replacing by the values, we get:

K= 3.62 KJ

4 0
3 years ago
You lift a 50 N object 2 meters off the ground what work did you do on the object
mixer [17]
Work equals force × displacement (distance between initial point and end point is displacement)
if u follow this it becomes
work = 50 × 2 which is equal to 100

comment if u have more questions
4 0
3 years ago
What is A common source of stress?
Oksanka [162]

Answer:

school, relashonships, etc.

Explanation:

5 0
3 years ago
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A glass window 0.33 cm thick measures 87 cm by 36 cm. How much heat flows through this window per minute if the inside and outsi
mojhsa [17]

Answer:

6.38 x 10^4 J

Explanation:

d = 0.33 cm = 0.33 x 10^-2 m, Area = 87 x 36 cm^2 = 0.87 x 0.36 m^2

ΔT = 14 degree C, t = 1 min = 60 second

K = 0.8 W / m K

Heat  = K A ΔT t / d

H = 0.8 x 0.87 x 0.36 x 14 x 60 / (0.33 x 10^-2)

H = 6.38 x 10^4 J

7 0
3 years ago
A spring vibrates 120 times in 2 mins find its frequency and time period​
german

2 minutes is 120 seconds, so if you were finding vibrations per minute, it would be 60 times a minute.

3 0
2 years ago
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