A 4-kg object moving 12 m/s in the positive x direction has a one-dimensional elastic collision with an object (mass = M) initially at rest. After the collision the object of unknown mass has a velocity of 6.0 m/s in the positive x direction. What is M
please need help ASAP
initial momentum = 4 * 12 = 48
initial Ke = (1/2) * 4 * 144 = 288
final momentum = 48 = 4 * v + M * 6 = 6 M + 4 v
final Ke = (1/2)* 4 * v^2 + (1/2) M * 36 = 2 v^2 + 18 M = 288 if perfectly elastic
v = (48 - 6 M)/4 = 12 - 1.5 M
2 (12 - 1.5 M)^2 + 18 M = 288
2(144 - 36M + 2.25M*2) + 18M = 288
288 - 72 M +4.5 M*2 + 18 M = 288
4.5 M^2 -54 M = 0
M(4.5 M -54) = 0
M = 0 or M = 54/4.5 = 12
thanks alottttt
To find the mass of the object (M) after the collision, we can use the law of conservation of linear momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is defined as the product of its mass (m) and velocity (v):
p = mv
Before the collision, the momentum of the 4-kg object moving at 12 m/s is:
p1 = (4 kg) * (12 m/s) = 48 kg.m/s
After the collision, the momentum of the object with mass M moving at 6.0 m/s is:
p2 = M * 6.0 m/s
Since the collision is elastic and there is no loss of kinetic energy, the total momentum before and after the collision must be the same. Therefore, we can equate the two momenta:
p1 = p2
48 kg.m/s = M * 6.0 m/s
Now we can solve for M by rearranging the equation:
M = 48 kg.m/s / 6.0 m/s
M = 8 kg
Therefore, the mass of the object (M) after the collision is 8 kg.
To find the mass of the object (M) after the collision, we can use the principle of conservation of linear momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
The momentum of the 4-kg object moving at 12 m/s can be calculated using the formula: momentum = mass × velocity.
So, the momentum before the collision for the 4-kg object is: momentum1 = 4 kg × 12 m/s = 48 kg·m/s.
Since the second object is initially at rest, its momentum before the collision is zero: momentum2 = 0 kg·m/s.
Therefore, the total momentum before the collision is: momentum_total = momentum1 + momentum2 = 48 kg·m/s + 0 kg·m/s = 48 kg·m/s.
After the collision:
The momentum of the object with mass M after the collision can be determined using the same formula: momentum = mass × velocity.
So, the momentum after the collision for the object with mass M is: momentum_after_collision = M kg × 6.0 m/s.
According to the principle of conservation of linear momentum, the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can set up the equation:
momentum_total = momentum_after_collision
48 kg·m/s = M kg × 6.0 m/s
To solve for M, we can rearrange the equation:
M = (48 kg·m/s) / (6.0 m/s)
M = 8 kg
Therefore, the mass of the object (M) after the collision is 8 kg.