A tennis player places a 51 kg ball machine on a frictionless surface, as shown below. The machine fires a 0.067 kg tennis ball horizontally with a velocity of 33.4 m/s toward the north. What is the final velocity of the machine?
Newton's first law
Momentum before = 0
momentum after = momentum before = 0
51 v + .067 * 33.4 = 0
You got 0? how?
No, the sum of those two terms is 0
51 v = - .067*33.4
v = -.067*33.4/51
thanks i got it(:
To find the final velocity of the machine, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. According to the conservation of momentum, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this case, we have the 51 kg ball machine and the 0.067 kg tennis ball. Let's assume that the final velocity of the machine is v_m, and the final velocity of the tennis ball is v_b.
Before the event, the ball machine is at rest, so its initial velocity (v_m_initial) is 0 m/s. The tennis ball has an initial velocity (v_b_initial) of 33.4 m/s toward the north.
Using the conservation of momentum, we can write the equation:
(m_m * v_m_initial) + (m_b * v_b_initial) = (m_m * v_m) + (m_b * v_b)
Substituting the given values:
(51 kg * 0 m/s) + (0.067 kg * 33.4 m/s) = (51 kg * v_m) + (0.067 kg * v_b)
Simplifying the equation, we get:
0 kg·m/s + 2.2388 kg·m/s = 51 kg·v_m + 0.067 kg·v_b
Since the machine is placed on a frictionless surface, there are no external forces acting on it or the tennis ball. Therefore, the momentum of the system is conserved.
As a result, we can write the equation as:
2.2388 kg·m/s = 51 kg·v_m + 0.067 kg·v_b
To find the final velocity of the machine (v_m), we need to know the final velocity of the tennis ball (v_b). However, it is not provided in the question. Without the value of v_b, we cannot determine the final velocity of the machine.