A 5-kg ball is at rest when it is struck head-on by a 2-kg ball moving along a track at 10 m/s. If the 2-kg ball is at rest after the collision, what is the speed of the 5-kg ball after the collision?
V1,f= 4 m/s
Well, let's see. This sounds like a classic case of physics in action! If the 2-kg ball is at rest after the collision, it must have transferred all its momentum to the 5-kg ball. And since momentum is conserved, we can use that fact to solve this puzzle!
The momentum of an object is given by the formula p = mass x velocity. So, before the collision, the 2-kg ball had a momentum of 2 kg * 10 m/s = 20 kg*m/s.
After the collision, if the 2-kg ball is at rest, all that momentum got transferred to the 5-kg ball. So, 20 kg*m/s = 5 kg * v (where v is the velocity of the 5-kg ball).
Solving for v, we find v = 20 kg*m/s / 5 kg = 4 m/s.
So, after the collision, the 5-kg ball will be rolling away with a speed of 4 m/s. Watch out for that ball! It might be on a roll!
To solve this problem, we can use the principles of conservation of momentum. In a closed system, the total momentum before a collision is equal to the total momentum after the collision.
Step 1: Calculate the initial momentum of the system before the collision.
The initial momentum is given by the product of mass and velocity.
The momentum of the 5-kg ball is 0 kg*m/s since it is at rest.
The momentum of the 2-kg ball is (2 kg) * (10 m/s) = 20 kg*m/s.
So, the initial momentum of the system is 0 kg*m/s + 20 kg*m/s = 20 kg*m/s.
Step 2: Calculate the final momentum of the system after the collision.
Since the 2-kg ball is at rest after the collision, its momentum is 0 kg*m/s.
The momentum of the 5-kg ball after the collision is denoted by V (unknown speed) and can be calculated as (5 kg) * V.
So, the final momentum of the system is 0 kg*m/s + (5 kg) * V = 5V kg*m/s.
Step 3: Apply the principle of conservation of momentum.
According to the principle of conservation of momentum, the initial momentum of the system (20 kg*m/s) is equal to the final momentum of the system (5V kg*m/s).
So, 20 kg*m/s = 5V kg*m/s.
Step 4: Solve for the speed of the 5-kg ball after the collision.
Divide both sides of the equation by 5 kg to solve for V:
(20 kg*m/s) / (5 kg) = V.
4 m/s = V.
Therefore, the speed of the 5-kg ball after the collision is 4 m/s.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before a collision is equal to the total momentum after the collision.
Momentum is defined as the product of an object's mass and its velocity. In this problem, the momentum before the collision is the sum of the momenta of the 5-kg ball and the 2-kg ball.
Let's denote the velocity of the 5-kg ball after the collision as v (m/s). Since the 2-kg ball is at rest after the collision, its final velocity is 0 m/s.
According to the conservation of momentum, the sum of the initial momenta is equal to the sum of the final momenta:
(Initial momentum of 5-kg ball) + (Initial momentum of 2-kg ball) = (Final momentum of 5-kg ball) + (Final momentum of 2-kg ball)
The initial momentum of the 5-kg ball is 0, as it is at rest. The initial momentum of the 2-kg ball is given by its mass (2 kg) multiplied by its initial velocity (10 m/s):
(2 kg) x (10 m/s) = 20 kg·m/s
The final momentum of the 2-kg ball is 0, as it is at rest. The final momentum of the 5-kg ball is given by its mass (5 kg) multiplied by its final velocity (v m/s):
(5 kg) x (v m/s) = 5v kg·m/s
Using the conservation of momentum equation, we can now solve for the final velocity of the 5-kg ball:
20 kg·m/s = 5v kg·m/s
Dividing both sides of the equation by 5 kg, we get:
4 m/s = v
Therefore, the speed of the 5-kg ball after the collision is 4 m/s.