Block A (mass = 3 kg), moving at +5 meters per second, collides with stationary block B (mass = 4 kg). Block A comes to a sudden stop, while block B starts moving. What will be the approximate final speed of block B?
conserve momentum:
3*5 + 4*0 = 3*0 + 4v
3.8
To determine the final speed of block B, we can apply the principles of conservation of momentum and solve for the final velocity.
1. First, let's calculate the initial momentum of block A before the collision. Momentum is defined as the product of an object's mass and its velocity. Therefore, the initial momentum of block A is given by:
Momentum(A, initial) = mass(A) * velocity(A, initial)
= 3 kg * 5 m/s
= 15 kg m/s
2. Next, let's calculate the initial momentum of block B. Since block B is stationary initially, its initial velocity is 0. Therefore, the initial momentum of block B is:
Momentum(B, initial) = mass(B) * velocity(B, initial)
= 4 kg * 0 m/s
= 0 kg m/s
3. The total initial momentum before the collision is the sum of the initial momentum of block A and block B:
Total initial momentum = Momentum(A, initial) + Momentum(B, initial)
= 15 kg m/s + 0 kg m/s
= 15 kg m/s
4. According to the conservation of momentum principle, the total momentum after the collision should be equal to the total initial momentum. Since block A comes to a sudden stop, its final velocity is 0. Therefore, the final momentum of block A is:
Momentum(A, final) = mass(A) * velocity(A, final)
= 3 kg * 0 m/s
= 0 kg m/s
5. Now, we can solve for the final velocity of block B. Using the conservation of momentum:
Total initial momentum = Total final momentum
15 kg m/s = Momentum(B, final)
Solving for the final momentum of block B:
Momentum(B, final) = 15 kg m/s
6. Finally, let's calculate the final velocity of block B. Using the equation for momentum:
Momentum(B, final) = mass(B) * velocity(B, final)
15 kg m/s = 4 kg * velocity(B, final)
Solving for the final velocity of block B:
velocity(B, final) = 15 kg m/s / 4 kg
= 3.75 m/s
Therefore, the approximate final speed of block B after the collision is 3.75 m/s.