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A truck is moving under a hopper with a constant speed of 20m/s. Sand falls on the truck at a rate $20kg{s^{ - 1}}$. What is the force acting on the truck due to falling sand?

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Last updated date: 14th Apr 2024
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MVSAT 2024
Answer
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Hint: This numerical problem can be solved by using Newton’s Second law of motion. According to Newton’s second law of motion; Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. Acceleration of an object depends on two things, force and mass.

Formula Used:
According to the mathematical formulation of Newton’s second law of motion, we know that the force acting is equal to the product of the mass and acceleration of the body. Thus:
\[F = m \times a\]
In this equation: $m$ is the mass of the body and $a$ is the acceleration of the body.

Complete step by step answer:
In this numerical problem it is given that the velocity of the truck is equal to $20m{s^{ - 1}}$. Now, the mass of the sand falling is $20kg$ and the time taken for it to happen is $1\sec $.
Now, the acceleration of the sand is equal to $20m{s^{ - 2}}$.
We can now substitute these values in the mathematical expression for Newton’s second law of motion. Doing this we get:
$F = 20 \times 20 = 400N$

Thus, the force acting on the truck due to the falling sand is equal to $400N$.

Additional Information:
The acceleration is directly proportional to the net force; the net force equals mass times acceleration; the acceleration in the same direction as the net force; an acceleration is produced by a net force. It is the net force that is related to acceleration. The net force is the vector sum of all the forces. If all the individual forces acting upon an object are known, then the net force can be determined.

Note: It should be noted that the direction of the Force will be opposite to the motion of the truck since the sand falls on the truck. Thus, direction of the force of the truck can also be negative depending upon the frame of reference that we are basing it on.