A 5.9 g coin sliding to the right at 27.6 cm/s makes an elastic head-on collision with a 17.7 g coin that is initially at rest. After the collision, the 5.9 g coin moves to the left at 13.8 cm/s.
(a) Find the final velocity of the other coin.
(b) Find the amount of kinetic energy transferred to the 17.7 g coin.
The answer to (a) is 13.8.... can't get(b)
(a)
v₂= 2m₁v₁₀/(m₁+m₂) =2•5.9•27.6/(5.9+17.7)=13.8 cm/s
(b) KE1(fin) –KE1(init) =m₁ •v₁₀²/2 –m₁•v₁²/2=0.5•m₁ (v₁₀² –v₁²)=
=0.5•0.0059•(0.278²-0.138²)=1.7 •10⁻⁴ J.
or
KE2(fin)-KE2(init) = KE2(fin) -0 = m₂ •v₂²/2=0.0177•0.138²/2=1.7•10⁻⁴ J
are you sure the 0.138 shouldn't be .0138?? and the answer be 1.7e-6??
oh nvm
To find the final velocity of the other coin in part (a) of the question, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity.
Let's denote the mass of the 5.9 g coin as m1 = 5.9 g = 0.0059 kg and its initial velocity as v1 = 27.6 cm/s = 0.276 m/s.
Similarly, let's denote the mass of the 17.7 g coin as m2 = 17.7 g = 0.0177 kg and the final velocity of this coin as v2 (what we want to find).
Since the collision is elastic, kinetic energy is conserved as well. This allows us to solve part (b) of the question.
Now, applying the principle of conservation of momentum:
m1 * v1 + m2 * 0 = m1 * (-13.8 cm/s) + m2 * v2
(Here, note that the final velocity of the 5.9 g coin is given as -13.8 cm/s, indicating that it moves to the left)
Simplifying this equation, we have:
(m1 * v1) = (m1 * (-13.8 cm/s)) + (m2 * v2)
0.0059 kg * 0.276 m/s = 0.0059 kg * (-13.8 cm/s) + 0.0177 kg * v2
0.0016284 kg m/s = -0.0008142 kg m/s + 0.0177 kg * v2
0.0014422 kg m/s = 0.0177 kg * v2
Dividing both sides by 0.0177 kg:
v2 ≈ 0.0814 m/s
So, the final velocity of the 17.7 g coin is approximately 0.0814 m/s.
To find the amount of kinetic energy transferred to the 17.7 g coin in part (b) of the question, we can subtract the initial kinetic energy of the coin from its final kinetic energy.
The initial kinetic energy of the 17.7 g coin is zero since it is initially at rest.
The final kinetic energy of the 17.7 g coin is given by:
Kinetic energy = (1/2) * m * v^2
where m is the mass of the coin and v is its final velocity.
Plugging in the values, we have:
Kinetic energy transferred = (1/2) * m2 * v2^2
Kinetic energy transferred = (0.5) * 0.0177 kg * (0.0814 m/s)^2
Kinetic energy transferred ≈ 0.00006012 J
Thus, the amount of kinetic energy transferred to the 17.7 g coin is approximately 0.00006012 Joules.