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Sedbober [7]
3 years ago
9

A proton is traveling to the right at 2.0 * 107 m/s. It has a head on perfectly elastic collision with a carbon atom. The mass o

f the carbon atom is 12 times the mass of the proton.
What are the speed and direction of each after the collision?

Physics
2 answers:
mars1129 [50]3 years ago
8 0

Answer:

(a) v_{fC} = 3.1\times 10^{- 6}\ m/s, in the initial direction of the proton.

(b) v_{fp} - 3.7\times 10^{- 5}\ m/s, in the opposite direction.

Solution:

As per the question:

Velocity of the proton, v_{ip} = 2.0\times 10^{7}\ m/s

If,

Mass of proton  be m_{p}

Then

Mass of carbon atom, m_{C} = 12m_{p}

Now, if the initial velocity of the proton be v_{ip}

Let the carbon atom be initially at rest with initial velocity v_{iC} = 0\ m/s

As the collision is perfectly elastic:

Using the principle of conservation of linear momentum:

m_{p}v_{ip} + m_{c}v_{iC} = m_{p}v_{fp} + m_{c}v_{fC}

v_{fp} = 2.0\times 10^{7} - 12v_{fC}             (1)

Using the conservation of energy:

\frac{1}{2}m_{p}v_{ip}^{2} + \frac{1}{2}m_{c}v_{iC}^{2} = \frac{1}{2}m_{p}v_{fp}^{2} + \frac{1}{2}m_{c}v_{fC}^{2}

\frac{1}{2}m_{p}v_{ip}^{2} + 0 = \frac{1}{2}m_{p}v_{fp}^{2} + \frac{1}{2}12m_{p}v_{fC}^{2}

Using eqn (1):

(2.0\times 10^{7})^{2} = (2.0\times 10^{7} - 12v_{fC})^{2} + 12v_{fC}^{2}

Solving the above quadratic eqn, we get:

v_{fC} = 3.1\times 10^{- 6}\ m/s

Since, the velocity here is positive, i.e., the direction of the carbon atom is along the initial direction of proton.

Now, for the speed of the proton:

v_{fp} = 2.0\times 10^{7} - 12(3.1\times 10^{- 6}) = - 3.7\times 10^{- 5}\ m/s

Negative sign here indicates that the movement of the proton is in the opposite direction.

Nat2105 [25]3 years ago
6 0

Answer:

Vc = 17.83m/s

and Vp = 0.04m/s

This problems was solver by applying the principle of conservation of momentum and energy.

Explanation:

The kinetic energy is conserved.

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Define an element and give 5 examples of elements that are important to life .
fenix001 [56]

Answer:

A pure substance consisting only of atoms with the same number of protons in their nuclei-these appear on the periodic table

Oxygen

Hydrogen

Carbon

Sulfur

Phosphate

Nitrogen

Magnesium

Calcium

Potassium

Chlorine

(I know that these are more examples than needed, but you can use any)

8 0
2 years ago
What is epsilon zero and why does it come into use, particularly in the case of Gauss's Law?
Paha777 [63]
<span>Epsilon zero is permittivity of free space means how much air or vacuum permits electric field to travel from one charge to other.It is constant in the coulomb law. This allow Gauss's a lot easier to solve rather than using K</span>
5 0
3 years ago
A firecracker in a coconut blows the coconut into three pieces. Twopieces of equal mass fly off south and west, perpendicular to
loris [4]

Answer:

V = 13m/s

North-East (i.e. 45 degree from North)

Explanation:

This question deals with the idea of momentum.

Since the directions of a compass are fixed, we can take south as horizontal and west as vertical. Since both pieces of coconut are of equal mass, then the resultant of the two pieces would be in between South and West and the third piece would be opposite this direction and be in the North-East (i.e. 45 degree from North) direction

To find the speed of the third piece, we first find the speed on the two pieces of the coconut in terms of V_{x} (horizontal component of velocity) and V_{y} (vertical component of velocity)

We have

V_{y} = Velocity in South direction = 18m/s

m_{y} = Mass of piece in South direction = m

V_{x} = Velocity in West direction = 18m/s

m_{x} = Mass of piece in West direction = m

V_{ry} = Velocity of Third Piece in North direction = unknown

V_{rx} = Velocity of Third Piece in East direction = unknown

m = Mass of third piece = 2m

mV_{ry}  = m_{y} V_{y} \\ 2mV_{ry}  = m18\\ V_{ry} = 9

mV_{rx}  = m_{x} V_{x} \\ 2mV_{rx}  = m18\\ V_{rx} = 9

Since we now know the horizontal and vertical component of the velocity of the third piece of coconut we find the resultant velocity. Since we know the direction is North-East, we can imagine a right angled triangle with base of 9 and height 9 and the hypotenuse equal to the resultant velocity .

We can simply apply the Pythagoras theorem and find the hypotenuse

Hypotenuse^{2}  = Height^{2}  + Base^{2} \\ V_{3}^2  = 9^{2} + 9^{2} \\ V = 12.728 m/s

V = 13m/s

6 0
3 years ago
7) T F If two forces of equal magnitude act on an object that is hinged at a pivot, the force acting farther from the pivot must
saul85 [17]

Answer:

False

Explanation:

The torque exerted by a force is given by:

\tau=Fd sin \theta

where

F is the magnitude of the force

d is the distance between the point of application of the force and the pivot

\theta is the angle between the directions of F and d

We see that the magnitude of the torque depends on 3 factors. In this problem, we have 2 forces of equal magnitude (so, equal F). Moreover, one of the forces (let's call it force 1) acts farther from the pivot than force 2, so we have

d_1 > d_2

However, this does not mean that force 1 produces a greater torque. In fact, it also depends on the angle at which the force is applied. For instance, if the first force is applied parallel to d, then we have

\theta_1 =0\\sin \theta=0

and the torque produced by this force would be zero.

So, the statement is false.

4 0
3 years ago
8. A 3.0 x 10' g nerf projectile is fired from a 1.5 kg nerf gun. If the velocity of the projectile is
tatuchka [14]

Answer:

v_g=0.2\ m.s^{-1}

Explanation:

Given:

  • mass of nerf projectile, m_p=30\ g=0.03\ kg
  • velocity of nerf projectile, v_p=10\ m.s^{-1}
  • mass of the gun, m_g=1.5\ kg

Now in this case the collision can be assumed to be perfectly elastic.

<u>For an elastic collision:</u>

m_p.v_p=m_g.v_g

where:

v_g= recoil velocity of the gun

0.03\times 10=1.5\times v_g

v_g=0.2\ m.s^{-1}

4 0
2 years ago
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