In an inelastic collision, a steel ball of mass 200 g was hit hard into a large ball of dough of mass 700 g. The velocity of the steel ball was 25m/s. After the collision, the steel ball was stuck in the dough, and this combined system rolled for some time.
What was the velocity of the system of the steel ball and dough after the collision?
A) 5.6 m/s
B) 7.5 m/s
C) 8.8 m/s
D) 11.1 m/s
25 * 200 = v * 900
v = 5.55
so yes, A
it is 5.6m/s
To find the velocity of the steel ball and dough system after the collision, we can apply the principle of conservation of momentum.
The equation for conserving momentum is:
Initial momentum = Final momentum
The initial momentum is the momentum of the steel ball before the collision, which is given by the formula:
Initial momentum = mass of the steel ball * initial velocity of the steel ball
Substituting the given values:
Initial momentum = 0.2 kg * 25 m/s
Now, let's consider the final momentum of the system after the collision. Since the steel ball becomes stuck in the dough and the two objects move together, their final momentum is the sum of their individual momenta. The mass of the system is the combined mass of the steel ball and the dough:
Combined mass = mass of the steel ball + mass of the dough
= 0.2 kg + 0.7 kg
= 0.9 kg
The final momentum is then:
Final momentum = Combined mass * final velocity of the system
Let's substitute this into the conservation of momentum equation:
Initial momentum = Final momentum
0.2 kg * 25 m/s = 0.9 kg * final velocity
Simplifying the equation:
5 kg⋅m/s = 0.9 kg * final velocity
Dividing both sides by 0.9 kg:
5 kg⋅m/s / 0.9 kg = final velocity
Final velocity = 5.56 m/s (rounded to two decimal places)
So, the velocity of the system of the steel ball and dough after the collision is approximately 5.56 m/s.
Therefore, the answer is A) 5.6 m/s.
To determine the velocity of the system after the collision, we can use the principles of conservation of momentum.
The momentum before the collision can be calculated by multiplying the mass of the steel ball (m1) by its velocity (v1):
Momentum before collision (p1) = m1 * v1
The momentum after the collision can be calculated by considering the fact that the steel ball and the dough combine into a single system with a total mass (m1 + m2). Let's assume the velocity of the system after the collision is v2:
Momentum after collision (p2) = (m1 + m2) * v2
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
p1 = p2
So, we can set up an equation to solve for v2:
m1 * v1 = (m1 + m2) * v2
Now let's substitute the given values:
m1 = 200 g = 0.2 kg (convert grams to kilograms)
v1 = 25 m/s
m2 = 700 g = 0.7 kg
v2 = ?
0.2 kg * 25 m/s = (0.2 kg + 0.7 kg) * v2
Simplifying the equation:
5 kg*m/s = 0.9 kg * v2
v2 = 5 kg*m/s / 0.9 kg
v2 ≈ 5.56 m/s
Therefore, the velocity of the system of the steel ball and dough after the collision is approximately 5.6 m/s.
Hence, the correct answer is A) 5.6 m/s.