A 0.50 kg gold coin is sliding across a frictionless surface with velocity of 1.0 m/s due east when it collides with a 0.040 kg silver coin sliding at 5.0 m/s due northwest.
What is the question?
To solve this problem, we first need to calculate the total momentum before the collision, and then calculate the total momentum after the collision using the law of conservation of momentum.
Momentum is defined as the product of an object's mass and its velocity. The momentum of an object can be calculated using the equation:
momentum = mass × velocity
The momentum before the collision can be calculated by summing the individual momenta of both the gold and silver coins. Let's calculate the momentum of each coin separately.
For the gold coin:
Mass of the gold coin (m1) = 0.50 kg
Velocity of the gold coin (v1) = 1.0 m/s
Momentum of the gold coin (p1) = m1 × v1
For the silver coin:
Mass of the silver coin (m2) = 0.040 kg
Velocity of the silver coin (v2) = 5.0 m/s
Momentum of the silver coin (p2) = m2 × v2
Now, we can calculate the total momentum before the collision by summing p1 and p2:
Total momentum before collision = p1 + p2
Once we know the total momentum before the collision, we can use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. This allows us to calculate the velocity of the coins after the collision.
The conservation of momentum equation can be written as:
Total momentum before collision = Total momentum after collision
To find the velocities of the coins after the collision, we'll assume that both coins stick together after the collision. Let's call the final velocity of the coins v_f.
The total momentum after the collision can be calculated as:
Total momentum after collision = (m1 + m2) × v_f
Now, we can set up an equation using the conservation of momentum:
Total momentum before collision = Total momentum after collision
(p1 + p2) = (m1 + m2) × v_f
We can substitute the values we calculated earlier to solve for v_f:
(m1 × v1 + m2 × v2) = (m1 + m2) × v_f
Now, we can substitute the given values into the equation and solve for v_f.