On planet Tehar, the free-fall acceleration is the same as that on Earth but there is also a strong downward electric field that is uniform close to the planet's surface. A 2.00 kg ball having a charge of 5.00 µC is thrown upward at a speed of 29.2 m/s and it hits the ground after an interval of 4.40 s. What is the potential difference between the starting point and the top point of the trajectory?
To find the potential difference between the starting point and the top point of the trajectory, we need to consider both the gravitational potential energy and the electrical potential energy.
First, let's calculate the gravitational potential energy. The gravitational potential energy (Ug) is given by the equation:
Ug = m * g * h
Where m is the mass of the ball, g is the acceleration due to gravity, and h is the height difference.
Since the free-fall acceleration on planet Tehar is the same as that on Earth, g remains the same. The height difference (h) can be calculated using the equation:
h = v^2 / (2 * g)
Where v is the initial velocity of the ball.
Now, let's calculate the electrical potential energy. The electrical potential energy (Ue) is given by the equation:
Ue = q * V
Where q is the charge of the ball and V is the potential difference.
Next, we need to consider the conservation of energy. The total mechanical energy (Em) is the sum of the gravitational potential energy and the electrical potential energy:
Em = Ug + Ue
Since mechanical energy is conserved, the total mechanical energy at the starting point (Em1) is equal to the total mechanical energy at the top point (Em2):
Em1 = Em2
Substituting the equations for gravitational potential energy and electrical potential energy, we get:
m * g * h + q * V1 = m * g * h + q * V2
Simplifying the equation, we get:
V1 = V2
Therefore, the potential difference between the starting point and the top point of the trajectory is zero.