A pendulum is made of a small sphere of mass 0.250 kg attached to a lightweight string 1.20 m in length. As the pendulum swings

Answer:

0.018 J

Explanation:

The work required to bring the charge from infinity to the point P is equal to the change in its electric potential energy. This can be expressed as

where

represents the charge's magnitude

and signifies the potential difference between point P and infinity.

After substituting into the formula, we arrive at

a)

b) 803.4 N

Explanation:

a) At point C (top of the loop), the pilot experiences weightlessness, leading to the normal force from the seat being zero:

N = 0

Consequently, the force balance equation at position C becomes:

where the left term signifies the pilot's weight and the right term represents the centripetal force, with:

= acceleration due to gravity

= jet's velocity at the top

= loop radius

By solving for v,

Thus, this is the jet's speed at C.

The speed at position A (bottom) can be derived from

The distance traveled by the jet corresponds to half the circumference of the circle with radius r, therefore

Given the plane's deceleration is consistent, we can obtain it using the following equation:

b) The pilot experiences a force equal to the normal force from the seat. At point B (half-way through the loop), we find:

- The normal force from the seat, N, directed towards the center of the loop

- As there are no further forces acting toward the central axis, N must equal the centripetal force:

(1)

where

represents the speed at position B.

To deduce the velocity at B, we note that the distance covered by the jet between positions A and B is a quarter of a circle:

With knowledge of the deceleration, we can implement the equation of motion to find the velocity at the midway point B:

Thus, we then apply eq.(1) to determine the normal force acting on the pilot at B: