An air-track cart with mass m1=0.29kg and initial speed v0=0.95m/s collides with and sticks to a second cart that is at rest initially.
Part A
If the mass of the second cart is m2=0.55kg, how much kinetic energy is lost as a result of the collision?
Still need answer, above one is wrong
An air-track cart with mass m1=0.29kg and initial speed v0=0.95m/s collides with and sticks to a second cart that is at rest initially.
Part A
If the mass of the second cart is m2=0.55kg, how much kinetic energy is lost as a result of the collision?
Well, the kinetic energy is like that sneaky friend who loves to disappear without leaving a trace. In this collision, the initial kinetic energy of the first cart disappears and transforms into a mysterious form called potential energy. So, how much kinetic energy is lost? All of it! Poof! It's gone! Just like the last piece of cake at a party. But don't worry, the energy is still there in another form.
To find the kinetic energy lost as a result of the collision, we need to calculate the initial kinetic energy of the system (before the collision) and the final kinetic energy of the system (after the collision). The difference between the two will give us the kinetic energy lost.
Step 1: Calculate the initial kinetic energy
The initial kinetic energy is given by the formula:
K1 = (1/2) m1 v0^2
where K1 is the initial kinetic energy, m1 is the mass of the first cart, and v0 is the initial speed of the first cart.
Plugging in the given values:
K1 = (1/2) * 0.29 kg * (0.95 m/s)^2
Simplifying:
K1 = 0.5 * 0.29 kg * 0.9025 m^2/s^2
K1 = 0.1300225 J
Step 2: Calculate the final kinetic energy
After the collision, the two carts stick together and move as one unit.
The final kinetic energy of the system is given by the formula:
K2 = (1/2) (m1 + m2) v^2
where K2 is the final kinetic energy, m1 is the mass of the first cart, m2 is the mass of the second cart, and v is the final velocity of both carts after the collision.
Since the two carts stick together, their final velocity is the same. Therefore, we can calculate the final velocity using the principle of conservation of momentum.
Step 3: Apply conservation of momentum
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
The momentum before the collision is given by:
P1 = m1 v0
where P1 is the initial momentum.
The momentum after the collision is given by:
P2 = (m1 + m2) v
where P2 is the final momentum and v is the final velocity.
Setting the two expressions equal to each other:
m1 v0 = (m1 + m2) v
Solving for v:
v = (m1 v0) / (m1 + m2)
Plugging in the given values:
v = (0.29 kg * 0.95 m/s) / (0.29 kg + 0.55 kg)
v = 0.2767 m/s
Step 4: Calculate the final kinetic energy
Using the value of the final velocity obtained, we can now calculate the final kinetic energy K2:
K2 = (1/2) (m1 + m2) v^2
K2 = 0.5 * (0.29 kg + 0.55 kg) * (0.2767 m/s)^2
K2 = 0.5 * 0.84 kg * 0.07653789 m^2/s^2
K2 = 0.0324551536 J
Step 5: Calculate the kinetic energy lost
The kinetic energy lost as a result of the collision is given by the difference between the initial and final kinetic energy:
Kinetic energy lost = K1 - K2
Kinetic energy lost = 0.1300225 J - 0.0324551536 J
Kinetic energy lost = 0.0975673464 J
So, the amount of kinetic energy lost as a result of the collision is approximately 0.0976 J.
Initial KE = 0.5*0.29*0.95^2
= 0.1308625
Final KE= (0.5*0.29*0.95^2)-(0.5*(0.29+0.55)*((0.29*0.95)/(0.29+0.55))^2)
= 0.0451787
lost in the collision= Final KE - Initial KE
= 0.0451787-0.1308625
= -0.08568 J -------> Answer
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