Space Curvilinear Motion Problems

What is the magnitude of acceleration as passengers pass position A on the corkscrew ride?

At the bottom of the vertical loop, which of the following represents the correct radius of curvature?

Which value correctly represents the speed of the airplane at the bottom of the vertical loop?

What is the angle between the line of sight from spacecraft S to Mars and the trajectory b-b?

What is the recorded value of acceleration $ ddot{R}$ at the bottom of the loop?

What is the angle $ ddot{ heta}$ at the bottom of the vertical loop in radians per second squared?

Which force results in block B accelerating to the right at 3 m/s²?

What is the absolute velocity of point C relative to block A?

What is the relative velocity of block B with respect to block A?

At what angle is the spacecraft S approaching the planet Mars during its trajectory?

Problem 9

Passengers ride the 'Corkscrew' amusement ride which travels through a cylindrical helix
The velocity at position A is 15 m/s
The cylindrical helix has an effective radius of 5 meters
The helix angle is 40 degrees
The acceleration of the passengers at point A is 27.5 m/s^2
This problem is related to space curvilinear motion, in particular, cylindrical coordinates

Problem 10

An airplane flies through a vertical loop in the x-y plane
The airplane's speed at the bottom of the loop is 600 km/h
The loop has a radius of curvature of 1200 meters
The rate of change of the radius (( \dot{R} )) is 34.4 m/s^2
The angular acceleration (( \ddot{\theta} )) of the plane at the bottom of the loop is 0.01038 rad/s^2
This problem is related to space curvilinear motion, in particular, spherical coordinates

Problem 11

A spacecraft ( S ) approaches Mars along a trajectory
The spacecraft's velocity is 19 km/s
Mars' velocity is 24.1 km/s
The angle between the spacecraft's trajectory and Mars' orbital plane is 15 degrees
( \beta ) is the angle between the line of sight ( S-M ) and the spacecraft's trajectory ( b-b )
( \beta ) is calculated to be 55.6 degrees.
This problem is related to relative motion

Problem 12

Block B accelerates to the right at a constant rate of 3 m/s^2 due to a force ( P )
Block B's velocity is 2 m/s to the right
Block B's acceleration is 0.5 m/s^2
Block A's acceleration is 0.75 m/s^2
The absolute velocity of point C is 1 m/s to the right
The velocity of Block B relative to Block A ( v_{B/A} ) is 0.5 m/s
This problem is about the constrained motion of connected particles

Test your understanding of space curvilinear motion with these problems focused on cylindrical and spherical coordinates. You'll analyze scenarios involving amusement rides, airplanes, and spacecraft trajectories. Tackle these challenges to sharpen your physics skills in motion analysis.