A 2.00-kg blob of putty moving at 3.00m/s slams into a 4.00-g blob of putty at rest. Calculate the speed of the two stuck-together blobs of putty immediately after colliding
Above calculation off...need pay attention to weights:
A 2.00-KILOGRAM blob of putty moving at 3.00m/s slams into a 4.00-GRAM blob of putty at rest. Calculate the speed of the two stuck-together blobs of putty immediately after:
momentum before = 2 * 3 + 0.004*0 = 6.004
momentum after = 2.4 kg * v
To calculate the speed of the two stuck-together blobs of putty immediately after colliding, we can apply the principle of conservation of momentum.
The momentum before the collision is given by the equation:
𝑚₁𝑣₁ + 𝑚₂𝑣₂ = 𝑃
where m₁ and m₂ are the masses of the two blobs of putty, v₁ and v₂ are their initial velocities, and P is the total momentum before the collision.
Given:
m₁ = 2.00 kg (mass of the moving blob of putty)
v₁ = 3.00 m/s (initial velocity of the moving blob of putty)
m₂ = 4.00 g = 0.004 kg (mass of the stationary blob of putty)
v₂ = 0 m/s (initial velocity of the stationary blob of putty)
We can rearrange the equation to solve for P:
𝑃 = 𝑚₁𝑣₁ + 𝑚₂𝑣₂
𝑃 = (2.00 kg)(3.00 m/s) + (0.004 kg)(0 m/s)
𝑃 = 6.00 kg·m/s + 0 kg·m/s
𝑃 = 6.00 kg·m/s
The total momentum of the system before the collision is 6.00 kg·m/s.
According to the principle of conservation of momentum, the total momentum after the collision should also be 6.00 kg·m/s. Since the two blobs stick together after the collision, their combined mass can be used to find the final velocity.
Let's assume the final velocity of the stuck-together blobs is v_final.
𝑃 = (𝑚₁ + 𝑚₂)𝑣_final
By applying this equation, we can solve for the final velocity:
6.00 kg·m/s = (2.00 kg + 0.004 kg)𝑣_final
6.00 kg·m/s = 2.004 kg·𝑣_final
Dividing both sides of the equation by 2.004 kg:
𝑣_final = 6.00 kg·m/s / 2.004 kg
𝑣_final ≈ 2.995 m/s
Therefore, the speed of the two stuck-together blobs of putty immediately after colliding is approximately 2.995 m/s.
To calculate the speed of the two stuck-together blobs of putty immediately after colliding, 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.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = mv.
Let's break down the problem step by step:
Step 1: Determine the momentum of the first blob of putty (m1v1)
- Mass of the first blob (m1) = 2.00 kg
- Velocity of the first blob (v1) = 3.00 m/s
- Momentum of the first blob (p1) = m1 * v1
Step 2: Determine the momentum of the second blob of putty (m2v2)
- Mass of the second blob (m2) = 0.004 kg (since it's given as 4.00 g)
- Velocity of the second blob (v2) = 0 m/s (at rest)
- Momentum of the second blob (p2) = m2 * v2
Step 3: Calculate the total momentum before the collision (p_total_initial)
- p_total_initial = p1 + p2
Step 4: Calculate the total mass after the collision (m_total)
- Since the two blobs stick together, the total mass after the collision will be the sum of their individual masses: m_total = m1 + m2
Step 5: Determine the velocity of the two stuck-together blobs after the collision (v_final)
- Using the law of conservation of momentum: p_total_initial = m_total * v_final
- Rearrange the equation to solve for v_final: v_final = p_total_initial / m_total
Now let's plug in the values and calculate the result:
Step 1: Momentum of the first blob
- p1 = m1 * v1 = 2.00 kg * 3.00 m/s = 6.00 kg·m/s
Step 2: Momentum of the second blob
- p2 = m2 * v2 = 0.004 kg * 0 m/s = 0 kg·m/s
Step 3: Total momentum before the collision
- p_total_initial = p1 + p2 = 6.00 kg·m/s + 0 kg·m/s = 6.00 kg·m/s
Step 4: Total mass after the collision
- m_total = m1 + m2 = 2.00 kg + 0.004 kg = 2.004 kg
Step 5: Velocity of the two stuck-together blobs after the collision
- v_final = p_total_initial / m_total = 6.00 kg·m/s / 2.004 kg ≈ 2.996 m/s
Therefore, the speed of the two stuck-together blobs of putty immediately after colliding is approximately 2.996 m/s.
momentum before = 2 * 3 + 4*0 = 6
momentum after = 6 kg * v
so
6 v = 6
v = 1 m/s