A 50 g ball of clay traveling east at 3.5 m/s collides and sticks together with a 50 g ball of clay traveling north at 2.0 m/s. What is the speed of the resulting ball of clay?
((m1)(v1))i+((m2)(v2))i =(m1+m2)Vf
[(0.05kg)(0)+(0.05kg)(2.0m/s)]
/[(0.05kg+0.05kg)]=1.0 m/s .........(east)
[(0.05kg)(3.5m/s)+(0.05kg)(0m/s)]
/[0.05kg+0.05kg)]= 17 m/s............(north)
(1)^2+(17)^2 = Vf^2
Vf=Sqrt[(1^2)+(17^2)]
Vf= 17.6 m/s
To find the speed of the resulting ball of clay after the collision, we need to use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is found by multiplying its mass by its velocity. Therefore, we need to calculate the momentum of each clay ball before the collision and then add them together to find the total momentum.
First, let's calculate the momentum of the 50 g clay ball traveling east. We know its mass is 50 g, but we need to convert it to kilograms because the SI unit for mass is kilograms.
Given: mass = 50 g = 0.05 kg, velocity = 3.5 m/s
Momentum = mass × velocity
= 0.05 kg × 3.5 m/s
= 0.175 kg·m/s
Similarly, let's calculate the momentum of the 50 g clay ball traveling north.
Given: mass = 50 g = 0.05 kg, velocity = 2.0 m/s
Momentum = mass × velocity
= 0.05 kg × 2.0 m/s
= 0.1 kg·m/s
Now, we can find the total momentum before the collision by adding the momentum of both clay balls.
Total momentum before collision = momentum of east clay ball + momentum of north clay ball
= 0.175 kg·m/s + 0.1 kg·m/s
= 0.275 kg·m/s
According to the principle of conservation of momentum, the total momentum after the collision should be equal to the total momentum before the collision.
Total momentum before collision = Total momentum after collision
Since the two clay balls stick together after the collision, they combine to form one single ball of clay. Therefore, the mass of the resulting ball of clay is the sum of the masses of the individual balls (50 g + 50 g = 100 g = 0.1 kg). Let's assume the speed of the resulting ball of clay is v.
Total momentum after collision = (total mass of resulting clay ball) × v
Equating the total momentum before the collision with the total momentum after the collision, we have:
0.275 kg·m/s = 0.1 kg × v
Simplifying the equation, we find:
v = 0.275 kg·m/s / 0.1 kg
= 2.75 m/s
Therefore, the speed of the resulting ball of clay after the collision is 2.75 m/s.