object A of mass 3g with a velocity of 12cm/s to the east, collides with stationary object B. After collision, object A rebounds with a velocity of 10cm/s to the west and object B has a velocity of 1.5cm/s to the east. Calculate the mass of obeject B
m1 =3 g, v1 =12 cm/s, m2=?, v2 = 0,
u1 = -10cm/s, u2 =1.5 cm.
u1 =(m1-m2) •v1/(m1+m2),
u2 = 2•m1•v1/(m1+m2),
u1/u2 = (m1-m2) •v1/2•m1•v1.
(-10)/1.5 = (3 –m2) •12/2•3•12.
Solving for m2 we obtain
m2 =43 g.
To calculate the mass of object B, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Momentum (p) is defined as the product of mass (m) and velocity (v). So, the momentum of object A before the collision is given by:
p(A,before) = m(A) * v(A,before)
where:
m(A) is the mass of object A (given as 3g = 0.003kg)
v(A,before) is the velocity of object A before the collision (given as 12cm/s)
Therefore, the momentum of object A before the collision is:
p(A,before) = 0.003kg * 12cm/s
Similarly, the momentum of object A after the collision is:
p(A,after) = m(A) * v(A,after)
where:
v(A,after) is the velocity of object A after the collision (given as 10cm/s to the west, but we consider it as -10cm/s to account for direction)
Now, let's consider object B. Since it is initially stationary, its momentum before the collision is zero:
p(B,before) = 0
After the collision, object B has a velocity of 1.5cm/s to the east. Therefore, the momentum of object B after the collision is:
p(B,after) = m(B) * v(B,after)
where:
m(B) is the mass of object B (unknown)
v(B,after) is the velocity of object B after the collision (given as 1.5cm/s)
According to the conservation of momentum:
p(A,before) + p(B,before) = p(A,after) + p(B,after)
Substituting the given values:
0.003kg * 12cm/s + 0 = 0.003kg * (-10cm/s) + m(B) * 1.5cm/s
Now, let's solve the equation for the unknown mass m(B):
0.036kg*cm/s = -0.03kg*cm/s + 1.5cm/s * m(B)
0.036kg*cm/s + 0.03kg*cm/s = 1.5cm/s * m(B)
0.066kg*cm/s = 1.5cm/s * m(B)
Divide both sides by 1.5cm/s:
0.066kg*cm/s / 1.5cm/s = m(B)
m(B) = 0.044kg
Therefore, the mass of object B is 0.044kg.