Question

A block of metal weighing 2 kg is resting on a frictionless plane. It is struck by a jet releasing water at a rate of 1 kg/s and at a speed.

Answer 1

Hint: Momentum is the product of mass and velocity. Any object moving will have momentum in them. Determine the initial and final momentum of the body. Then apply it to find the force exerted by the block for one second. Then by using Newton's laws of motion determine the acceleration of the block of mass m.

Complete step by step answer:
Momentum can be defined as mass in motion. Momentum is the product of mass and velocity. Any object moving will have momentum in them. How fast the stuff is moving and how much stuff is moving tells us about the amount of momentum that an object contains.

Momentum depends on the mass and velocity. Momentum is known to be a vector quantity since it has both magnitude and direction. All objects have mass and all the objects are in motion hence the entire object has momentum. Force is defined using Newton's second law and we can define force as rate of change of momentum or the product of mass and acceleration.

The water is released in the rate of $\dfrac{{dm}}{{dt}} = 1kg/s$
The final velocity $v$ of water after hitting the block is zero $ie:v = 0$
Then the change in momentum is given by $m\left( {u - v} \right)$
Here $v$ is zero, so
$1 \times 5 = 5kgm/s$
Here the momentum occurs during 1 second. Then the force on the block is
$\dfrac{5}{1} = 5N$
Hence the acceleration of the block of mass from newton’s second law is
$a = \dfrac{F}{m} = \dfrac{5}{2} = 2.5m/{s^2}$

Note: Momentum is in sports commonly. Momentum can be defined as mass in motion. Momentum depends on the mass and velocity. Momentum is known to be a vector quantity since it has both magnitude and direction. Force determines the value of acceleration and mass.