# A ball with a mass of #5 kg# moving at #12 m/s# hits a still ball with a mass of #9 kg#. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

I found:

Have a look:

By signing up, you agree to our Terms of Service and Privacy Policy

To find the velocity of the second ball after the collision, you can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

The initial momentum is given by the formula: ( p = mv ) where ( p ) is momentum, ( m ) is mass, and ( v ) is velocity.

The total initial momentum before the collision is ( p_{\text{initial}} = m_1 \cdot v_1 + m_2 \cdot v_2 ).

After the collision, the first ball stops moving, so its final velocity ( v_1' = 0 ).

The total momentum after the collision is ( p_{\text{final}} = m_1 \cdot v_1' + m_2 \cdot v_2' ).

Using the conservation of momentum, we have ( p_{\text{initial}} = p_{\text{final}} ), which gives:

( m_1 \cdot v_1 + m_2 \cdot v_2 = m_1 \cdot v_1' + m_2 \cdot v_2' ).

Solving for ( v_2' ), the velocity of the second ball after the collision, we get:

( v_2' = \frac{m_1 \cdot v_1 + m_2 \cdot v_2 - m_1 \cdot v_1'}{m_2} ).

Plugging in the given values, ( m_1 = 5 ) kg, ( v_1 = 12 ) m/s, ( m_2 = 9 ) kg, and ( v_1' = 0 ) m/s, we can calculate ( v_2' ).

( v_2' = \frac{5 \cdot 12 + 9 \cdot 0 - 5 \cdot 0}{9} )

( v_2' = \frac{60}{9} )

( v_2' \approx 6.67 ) m/s

To find the kinetic energy lost as heat in the collision, you can use the formula for kinetic energy: ( KE = \frac{1}{2}mv^2 ), where ( KE ) is kinetic energy, ( m ) is mass, and ( v ) is velocity.

The initial kinetic energy before the collision is the sum of the kinetic energies of both balls, and the final kinetic energy after the collision is the sum of the kinetic energies of both balls.

The kinetic energy lost as heat in the collision is the difference between the initial and final kinetic energies.

Plugging in the given values, we can calculate the initial and final kinetic energies, then find the difference to determine the kinetic energy lost as heat.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- A 0.145 kg baseball is moving at 35 m/s it is caught by a player. What is the change in momentum of the ball?
- An astronaut with a mass of #75 kg# is floating in space. If the astronaut throws a #4 kg# object at a speed of #6 m/s#, how much will his speed change by?
- The velocity of an object with a mass of #8 kg# is given by #v(t)= sin 5 t + cos 3 t #. What is the impulse applied to the object at #t= ( 3 pi)/ 4 #?
- When a body falls, its momentum increases. Does this mean that the momentum is not conserved?
- A ball with a mass of #7 kg# moving at #4 m/s# hits a still ball with a mass of #12 kg#. If the first ball stops moving, how fast is the second ball moving?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7