A toboggan of mass 8.4 is moving horizontally at 18 . As it passes under a tree, 18 of snow drop onto it.
We're covering Momentum and collisions, and I have no idea where to start here.
You must provide dimensions with your numbers.
To solve this problem, we can use the principle of conservation of momentum. Momentum is a vector quantity that depends on both mass and velocity. The law of conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision.
Let's break down the problem into steps:
Step 1: Determine the initial momentum of the toboggan.
The initial momentum (p1) is equal to the product of mass (m1) and velocity (v1).
Given: mass (m1) = 8.4 kg and velocity (v1) = 18 m/s.
So, p1 = m1 * v1.
Step 2: Determine the momentum added to the toboggan by the snow.
The mass of the snow (m2) was not provided directly, but we are given its weight (18 N). We can use the formula:
Weight (W) = mass (m) * acceleration due to gravity (g).
Given: weight (W) = 18 N, and acceleration due to gravity (g) is approximately 9.8 m/s^2.
So, m2 = W / g.
Step 3: Determine the final velocity of the toboggan.
Since the snow dropped onto the toboggan horizontally, it only adds to the horizontal momentum. Therefore, the final momentum (p2) will only change in the horizontal direction.
The final momentum (p2) will be the sum of the initial momentum (p1) and the momentum added by the snow (p2).
Since momentum is a vector, the direction matters. In this case, since the snow dropped onto the toboggan horizontally, the direction is positive.
So, p2 = p1 + p2.
Step 4: Solve for the final velocity.
The final velocity (v2) can be found by dividing the final momentum (p2) by the mass (m1) of the toboggan.
So, v2 = p2 / m1.
Now, let's calculate the values:
Step 1: Initial momentum:
p1 = (8.4 kg) * (18 m/s) = 151.2 kg·m/s.
Step 2: Mass of the snow:
m2 = (18 N) / (9.8 m/s^2) ≈ 1.84 kg.
Step 3: Final momentum:
p2 = p1 + p2 = 151.2 kg·m/s + (1.84 kg) * (0 m/s) = 151.2 kg·m/s.
Step 4: Final velocity:
v2 = p2 / m1 = 151.2 kg·m/s / 8.4 kg ≈ 18 m/s.
Therefore, the final velocity of the toboggan is approximately 18 m/s.