A particle moving along the y-axis has the potential eneryg function U = 6 * y3 J where y is in m. What is the y-component of the force on the particle at 0 m?
What is the y-component of the force on the particle at 9 m?
What is the y-component of the force on the particle at 18 m?
The force is -dU/dy
Is the 3 after the y supposed to be an exponent? If so,
F = -18 y^2 Newtons
Plug in y values to get your answers.
To find the y-component of the force on the particle, we can use the relationship between potential energy and force. The force can be calculated by taking the negative derivative of potential energy with respect to y, i.e., F = -dU/dy.
Given that the potential energy function is U = 6 * y^3 J, we can differentiate it with respect to y to find the force function.
Taking the derivative of U with respect to y, we get dU/dy = 18 * y^2 J/m.
Now, let's calculate the y-component of the force on the particle at different values of y:
1. At y = 0 m:
Plugging y = 0 into the force function, we have F = -dU/dy = -18 * (0)^2 J/m = 0 J/m.
Therefore, the y-component of the force on the particle at 0 m is 0 J/m.
2. At y = 9 m:
Plugging y = 9 into the force function, we have F = -dU/dy = -18 * (9)^2 J/m = -1458 J/m.
Therefore, the y-component of the force on the particle at 9 m is -1458 J/m.
3. At y = 18 m:
Plugging y = 18 into the force function, we have F = -dU/dy = -18 * (18)^2 J/m = -5832 J/m.
Therefore, the y-component of the force on the particle at 18 m is -5832 J/m.
In summary:
- At 0 m, the y-component of the force is 0 J/m.
- At 9 m, the y-component of the force is -1458 J/m.
- At 18 m, the y-component of the force is -5832 J/m.