A solar system may form from a spinning disk of material called a(n _____

Response:

length = 2L, mass = M/2, and maximum angular displacement = 1 degree

Clarification:

We examine only small amplitude oscillations (as in this scenario), which keeps the angle θ sufficiently small. In such situations, it's important to note that the pendulum's motion can be described by the equation:

The resulting solution is:

Here, represents the angular frequency of the oscillations, enabling us to find the period:

As a result, the period of a pendulum is determined solely by its length and is independent of both its mass and angle, provided the angle remains small. Therefore, the choice with the longest length gives the longest period.

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:

Utilizing the acceleration formula,

d. at the same velocity. Explanation: I'll assume the car is also moving west since the helicopter is stated to be above it. From the perspective of someone in the car, the helicopter will appear stationary as they share the same velocity. Viewed from along the roadside, both are traveling at the same speed. Remember that velocity is a vector quantity, which includes direction, while speed measures the rate at which an object covers distance without direction. Hence, velocity is the appropriate term here.

In this scenario, there exists a constant electric field produced by a large sheet. This electric field can be defined as... The force acting on the ball due to this field acts horizontally, and this force must be counterbalanced by the horizontal tension component of the string to maintain equilibrium. Similarly, the vertical tension component in the string must equal the weight of the small sphere. Hence, we can derive two equations to illustrate this.