1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
IRINA_888 [86]
3 years ago
12

two billiard balls moving along the same line hit each other head-on. each has a mass of 0.220 kg; one has an initial velocity o

f 1.84 m/s, the other an initial velocity of 0.530 m/s. if the collision is elastic, what are their final velocities? ignore friction.
Physics
1 answer:
Tems11 [23]3 years ago
7 0

Hi there!

Since the collision is elastic, we must also satisfy the following condition:

Ei = Ef, or:

KEi = KEf

Begin by writing an expression for momentum. (p = mv) Remember that one ball's direction is negative; in this instance, we can let the second ball be moving LEFT.

mv1 + mv2 = mvf1 + mvf2

0.220(1.84) + 0.220(-.530) = 0.220(vf1 + vf2)

0.2882/0.220 = vf1 + vf2

1.31 = vf1 + vf2

Now, we can express this as a conservation of energy:

1/2mv1² + 1/2mv2² = 1/2mvf1² + 1/2mvf2²

Plug in values and simplify:

0.403315 = 1/2m(vf1² + vf2²)

Simplify further:

3.6665 = vf1² + vf2²

Use the equation derived from momentum above and solve for one variable:

vf2 = 1.31 - vf1

Plug in this expression for vf2:

3.6665 = vf1² + (1.31 - vf1)²

Expand:

3.6665 = vf1² + 1.7161 - 2.62vf1 + vf1²

Simplify:

1.9504 = -2.62vf1 + 2vf1²

Solve for vf1 using a graphing calculator:

vf1 = -0.53 m/s or 1.84 m/s; we must figure out which one is correct.

Since v1 is heading to the right initially with a velocity of 1.84 m/s, we know that the ball's velocity could not have stayed the same in both magnitude and direction, so the final velocity must be -0.53 m/s.

Now, we can solve for the velocity of the other ball (initial of 0.53 m/s):

vf2 = 1.31 - (-0.53) = 1.84 m/s.

Now, you could have also made the connection that when two balls of the SAME MASS experience an ELASTIC collision, the velocities are simply "exchanged" from one to another. I just used this more "extensive" method to prove this.

You might be interested in
A beam of light strikes one face of a window pane with an angle of incidence of 30.0°. The index of refraction of the glass is 1
natka813 [3]

Answer:

(a). The angle of refraction is 19.26°.

(b). That is proved that the rays in air on either side of the glass are parallel to each other

Explanation:

Given that,

Angle of incidence = 30.0°

Index of reflection of glass = 1.52

(a). We need to calculate the angle of refraction for the ray inside the glass

Using snell's law

\dfrac{\sin i}{\sin r}=\mu

\sin r=\dfrac{\sin i}{\mu}

Put the value into the formula

\sin r=\dfrac{\sin 30}{1.52}

r=\sin^{-1}(0.329)

r=19.26^{\circ}

(b). We know that,

The incident ray and emerging ray  is equal then the ray will be parallel.

We need to prove that the rays in air on either side of the glass are parallel to each other

Using formula for emerging ray

\dfrac{\sin e}{\sin r}=\mu

\sin e=\sin r\times \mu

Put the value into the formula

\sin e=0.3289\times 1.52

e=\sin^{-1}(0.499)

e=29.9\approx 30^{\circ}

So, \sin i=\sin e

This is proved.

Hence, (a). The angle of refraction is 19.26°.

(b). That is proved that the rays in air on either side of the glass are parallel to each other

6 0
3 years ago
In 1958 a large earthquake in Alaska produced a tsunami. What was the approximate height of the tsunami?
lilavasa [31]
The approximate height of the tsunami in Alaska in 1958 is 1720ft
6 0
3 years ago
Read 2 more answers
Matter is anything that has
Svetlanka [38]

Answer:

Space

Explanation:

Hope this helped

8 0
3 years ago
A superhero swings a magic hammer over her head in a horizontal plane. The end of the hammer moves around a circular path of rad
Korolek [52]

Answer:

9.21954 m/s

54 m/s²

Angle is zero

Explanation:

r = Radius of arm = 1.5 m

\omega = Angular velocity = 6 rad/s

The horizontal component of speed is given by

v_h=\omega r\\\Rightarrow v_h=6\times 1.5\\\Rightarrow v_h=9\ m/s

The vertical component of speed is given by

v_v=2\ m/s

The resultant of the two components will give us the velocity of hammer with respect to the ground

v=\sqrt{v_h^2+v_v^2}\\\Rightarrow v=\sqrt{9^2+2^2}\\\Rightarrow v=9.21954\ m/s

The velocity of hammer relative to the ground is 9.21954 m/s

Acceleration in the vertical component is zero

Net acceleration is given by

a_n=a_h=\omega^2r\\\Rightarrow a_n=6^2\times 1.5\\\Rightarrow a_n=54\ m/s^2

Net acceleration is 54 m/s²

As the acceleration is towards the center the angle is zero.

3 0
3 years ago
Brainliest if right.
jeka57 [31]

Answer:

the third law (for every action there is an equal and opposite reaction).

Explanation:

The skateboarder pushes backwards on the road (that is he applies a force on the road in a direction opposite the direction of intended motion). By Newton's third law, this action of the skateboarder causes an equal reaction of the road on the skateboarder in the opposite direction. Newton's third law states that action and reaction are equal but opposite in direction. So, the road in response to this backward force pushes the skateboarder in the forward direction causing the skateboarder and the skateboard to move in the forward direction.

5 0
3 years ago
Other questions:
  • A ray of light is incident on a flat surface of a block of polystyrene, with an index of refraction of 1.49, that is submerged i
    5·1 answer
  • Temperature and silica content determine the of magma.
    12·1 answer
  • A 32 kg child puts a 15 kg box into a 12 kg wagon. The child then pulls horizontally on the wagon with a force of 65 N. if the b
    7·1 answer
  • What force would have to win out in order for the Big Crunch to occur?
    13·1 answer
  • Calculate the maximum capillary rise/fall of mercury in a 0.5 mm radius glass capillary. Assume that the surface tension for mer
    10·1 answer
  • Can someone answer these physics questions
    15·1 answer
  • The deflection of prevailing winds and ocean currents in the northern hemisphere is called
    8·1 answer
  • How can we represent a narrow beam of light?
    15·2 answers
  • 50 POINTS/BRAINLIEST TO CORRECT!
    11·1 answer
  • What are the four eaemts
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!