Answer:
Torque,
Explanation:
It is given that,
Force acting on the particle,
Position of the particle,
We need to find the torque on the particle about the origin. It is equal to the cross product of position and the force. Its formula is given by :
The cross product of vectors is given by :
or
So, the torque on the particle about the origin . Hence, this is the required solution.
Answer:
(a) 34.6429J
(b) -1.57 m
(c) 4.71 m
Explanation:
The derivative of the potential energy with respect to the position is equal to the negative of the force, so:
Then, if we integer both sides, we get:
∫dU = -∫(7x - 11)dx
we know that U is equal to 26 J when x is zero, so:
Finally, the equation for the potential energy is:
Therefore, the maximum positive potential energy is the energy when x is equal to 11/7. That is because the equation of U is the equation of a parable, and the vertex in a parable is given by:
Where b is the number beside x and a is the number beside , Then, the value of maximum U is:
On the other hand, the negative and positive values of x where the potential energy is equal to zero is calculated as:
if we solve this using the quadratic equation, we get:
Finally, the negative and positive values of x where the potential energy is equal to zero are -1.5747 and 4.7175 respectively.