'An air rifle pellet of mass 2g is fired into a block of plasticine mounted on a model railway truck. the truck and plasticine have a mass of .1kg. The truck moves off after the pellet hits the plasticine with an initial velocity of .8m/s. calculate the momentum of the plasticine and truck after the collision. Hence work out the velocity of the pellet just before it hits the plasticine.'
First, we need to determine the momentum of the plasticine and truck after the collision. The momentum of an object is given by the mass of the object multiplied by its velocity (p = mv). In this case, the mass of the truck and plasticine is 0.1 kg, and the initial velocity is 0.8 m/s.
Momentum of truck and plasticine = (mass of truck + mass of plasticine) * initial velocity of truck and plasticine
= 0.1 kg * 0.8 m/s
= 0.08 kg*m/s
Now we know the initial momentum of the pellet before it hits the plasticine is equal to the momentum of the truck and plasticine after the collision (assuming no external forces are acting on the system). Thus, the initial momentum of the pellet, which is also equal to the final momentum of the truck and plasticine, is 0.08 kg*m/s.
We also know the mass of the pellet is 0.002 kg (2g converted to kg).
Momentum of pellet = mass of pellet * velocity of pellet just before it hits the plasticine
0.08 kg*m/s = 0.002 kg * velocity of pellet
Now we can solve for the velocity of the pellet just before it hits the plasticine:
Velocity of pellet = 0.08 kg*m/s / 0.002 kg
= 40 m/s
Therefore, the velocity of the pellet just before it hits the plasticine is 40 m/s.
To solve this problem, we can use the principles of conservation of momentum.
Step 1: Calculate the momentum of the plasticine and truck after the collision.
The formula for momentum is given by:
Momentum = mass x velocity
Given:
Mass of the pellet, m1 = 2g = 0.002 kg
Mass of the truck and plasticine, m2 = 0.1 kg
Initial velocity of the truck after collision, v2 = 0.8 m/s
First, let's calculate the final velocity of the pellet and truck using the conservation of momentum equation:
m1 x v1 + m2 x v2 = (m1 + m2) x v
We know that the initial velocity of the pellet, v1, is 0 m/s because it comes to rest after hitting the plasticine.
Therefore, the equation simplifies to:
0.002 kg x 0 m/s + 0.1 kg x 0.8 m/s = (0.002 kg + 0.1 kg) x v
0.08 kg m/s = 0.102 kg x v
Solving for v, we get:
v = (0.08 kg m/s) / 0.102 kg
v ≈ 0.784 m/s
So, the velocity of the pellet just before it hits the plasticine is approximately 0.784 m/s.
Step 2: Calculate the momentum of the plasticine and truck after the collision.
Momentum = mass x velocity
Momentum = (m1 + m2) x v
Momentum = (0.002 kg + 0.1 kg) x 0.784 m/s
Momentum ≈ 0.102 kg x 0.784 m/s
Momentum ≈ 0.080 kg m/s
Therefore, the momentum of the plasticine and truck after the collision is approximately 0.080 kg m/s.
To calculate the momentum of the plasticine and truck after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
1. First, let's calculate the initial momentum of the pellet.
Momentum (p) is defined as the product of mass (m) and velocity (v).
Given that the mass of the pellet is 2g, we need to convert it to kilograms by dividing by 1000.
So, the mass of the pellet (m) = 2g / 1000 = 0.002kg.
The initial velocity of the pellet (v) is not given directly, but we will calculate it later.
2. Next, let's calculate the initial momentum of the truck and plasticine.
The total mass of the truck and plasticine is given as 0.1kg.
The initial velocity of the truck is given as 0.8m/s.
Momentum (p) = mass (m) x velocity (v).
The initial momentum of the truck and plasticine is:
momentum = (mass of truck and plasticine) x (velocity of truck)
= 0.1kg x 0.8m/s.
3. According to the law of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
Therefore, the initial momentum of the pellet should be equal to the final momentum of the truck and plasticine.
4. Now, let's calculate the final momentum of the truck and plasticine.
Let the final velocity of the truck and plasticine be denoted as V.
The final momentum (after collision) of the truck and plasticine is:
Final momentum = (mass of truck and plasticine) x (final velocity of truck and plasticine)
= 0.1kg x V.
Since the initial momentum of the pellet is equal to the final momentum of the truck and plasticine (according to the conservation of momentum), we can set the two equations equal to each other:
0.002kg x (velocity of pellet) = 0.1kg x V
5. Rearrange the equation to solve for the velocity of the pellet just before it hits the plasticine:
(velocity of pellet) = (0.1kg x V) / 0.002kg
Now you can substitute the values and calculate the velocity of the pellet just before it hits the plasticine.