Aparticle moving along the y-axis has the potential energy u =4y3j, where y is in m. what is the y-component of the force on the particle at y=0 m, 1 m, and 2 m?

The force on the particle at

Explanation:

Given information:

The potential energy:

Now, as we know that force:

So, the gradient of energy with position y

At, y=0

.

At, y=1

At, y=2

Hence , The force on the particle at

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Potential energy is given as

now as we know that force is related by potential energy by the formula

So it is gradient of energy with position in Y

Now at y = 0

at y = 1

at y = 2

so above is the forces at given positions

v=ir = 3x15 =45 v