AP Physics 1 Vertical Loop Concepts

What must be true for the cart to remain on the track when it is at point P?

What must the student do to determine the inertial mass of the block?

How does the acceleration of the ball change as the radius of the circle decreases while keeping the tangential speed constant?

At what distance from the center of the Earth is the force of Earth's gravity on the payload W/2?

Why does the comet not travel in a circular path around the planet?

Which measuring devices are needed to experimentally determine the gravitational field strength of the object of mass m0?

What does Newton's second law of motion state for an object that experiences a centripetal force due to gravity?

What is a correct expression for the time T it takes the satellite to make one complete revolution around the moon?

What is the magnitude of the acceleration of the object of mass M at time t0?

How can the strength of the gravitational field on the planet be determined using the released object?

Forces and Motion in Circular Paths

For a cart on a vertical loop, the net force must equal or exceed the cart's weight at point P to remain on track.
A ball maintaining a constant tangential speed in a horizontal circle experiences increasing acceleration as the radius decreases due to the relationship ( a_c = \frac{v^2}{r} ).

Determining Inertial Mass

To find the inertial mass of a block being pulled on a horizontal surface, calculate the slope of the force vs. acceleration graph.

Gravitational Forces

A rocket lifting a payload experiences half the weight of the payload (( W/2 )) when it reaches a distance of ( \sqrt{2}R ) from the center of the Earth.
The behavior of a comet moving in a straight line near a planet suggests additional gravitational forces must be acting on it, balancing the gravitational influence of the planet.

Experimental Design

For measuring gravitational field strength in an experiment involving two masses, essential instruments include a mass balance, a meterstick, and a timer.

Newton's Laws

Newton's second law in the context of centripetal motion combines gravitational force and centripetal force through the equation ( \frac{GmM}{r^2} = \frac{mv^2}{r} ).

Orbital Mechanics

The time ( T ) for a satellite to complete one orbit around a moon can be determined with the formula ( T = 2\pi \sqrt{\frac{R^3}{GM}} ).

Acceleration on Inclined Circular Paths

For an object attached to a spinning disk, the magnitude of its acceleration is given by ( g \tan(\theta) ) at any point during its circular motion.

Gravitational Field Strength Calculation

To find the strength of the gravitational field on a planet, use the position-time equation ( y = y_0 + v_{y0}t + \frac{1}{2} a_y t^2 ) with specific parameters, solving for ( a_y ).

Kinetics of Sliding Objects

Understanding forces acting on an object (like a stone disk) helps analyze its motion when external forces, like a mallet, exert influence on it.

Test your understanding of the forces acting on a cart in vertical loops in this AP Physics 1 flashcard quiz. This quiz explores the conditions required for an object to maintain its path in circular motion when undergoing vertical circular motion. See if you can determine the necessary forces at play!