A block of metal weighing 2kg is resting on a frictionless plane. It is struck by a jet releasing water at the rate of 1kg/s and at a speed of 5m/s. Find the initial acceleration of the block.
You will have to make an assumption about what happens to the jet stream momentum as it splashes backwards. Since they don't tell you what to do, assume it loses all its momentum. The force on the block is then the mass flow rate times the incident velocity, or
F = 5 Newtons.
Use F = m a for the acceleration, a.
Jet releases water at the rate of 1 kg/sec
velocity = 5 m/s
Therefore force acting on the block = 1 x 5 = 5 N
acceleration = a = Force/Mass = 5/2 = 2.5 m/s2
To find the initial acceleration of the block, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The net force acting on the block can be determined by considering the water jet hitting the block. According to the law of conservation of momentum, the change in momentum of the water jet equals the change in momentum of the block.
The change in momentum of the water jet can be calculated using the formula:
Δp = m * v
where Δp is the change in momentum, m is the mass of the water jet, and v is its velocity. Given that the mass of the water jet is 1 kg and its velocity is 5 m/s, we can calculate the change in momentum:
Δp = 1 kg * 5 m/s = 5 kg⋅m/s
Since the block is initially at rest, its initial momentum is zero. Therefore, the change in momentum of the block is also 5 kg⋅m/s in the opposite direction.
Since the mass of the block is 2 kg, the net force acting on the block can be calculated using the formula:
F_net = Δp / Δt
where F_net is the net force, Δp is the change in momentum, and Δt is the time over which the momentum change occurred.
Given that the rate of water flow is 1 kg/s, we can determine that the time over which the momentum change occurred is 5 seconds.
Therefore, the net force acting on the block is:
F_net = 5 kg⋅m/s / 5 s = 1 N
Finally, we can calculate the initial acceleration of the block using the formula:
a = F_net / m
where a is the acceleration, F_net is the net force, and m is the mass of the block.
Substituting the values, we get:
a = 1 N / 2 kg = 0.5 m/s²
Hence, the initial acceleration of the block is 0.5 m/s².