A truck of mass 4×10^3 moving at 3.5 ms^-1 collides with a stationary truck to which it becomes automatically coupled. Immediately after the impact the trucks moves along together at 2 ms^-1 in the same direction. Find the mass of the second truck.
M1*V1 + M2*V2 = M1*V + M2*V.
4000*3.5 + M2*0 = 4000*2 + M2*2
14,000-8000 = 2M2
M2 = 3,000 kg.
To find the mass of the second truck, 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.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Before the collision, the momentum of the first truck (m1) is:
p1 = m1 * v1 = (4×10^3 kg) * (3.5 m/s) = 1.4×10^4 kg·m/s
Since the second truck is initially at rest, its momentum is zero:
p2 = m2 * v2 = 0 kg·m/s
Immediately after the collision, the two trucks move together with a velocity (v') of 2 m/s. The total momentum after the collision is given by the sum of the individual momenta of the trucks:
p_total = m1 * v' + m2 * v' = (1.4×10^4 kg·m/s) + m2 * (2 m/s)
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:
p_total = p1 + p2 = 1.4×10^4 kg·m/s
Therefore, we can equate the two expressions for p_total:
(1.4×10^4 kg·m/s) + m2 * (2 m/s) = 1.4×10^4 kg·m/s
Simplifying the equation, we find:
m2 * (2 m/s) = 0 kg·m/s
m2 = 0 kg
This implies that the mass of the second truck is zero, which doesn't make physical sense. It's important to note that there might be some additional information or constraints missing in the problem statement.