Vertical Centripetal Forces Practice Problems

A bridge on a bicycle racing track is shaped like an arc of a circle of radius 12.0 m. What should be the speed limit for a cyclist to avoid flying over the top of the bridge?

A bus loaded with students goes through a circular track with a radius of 19 m. When the bus reached its lowest point, a student claimed that her weight had doubled. Find the magnitude of the bus's velocity at the bottom of the track.

A marble goes around a loop-the-loop track by always being in contact with the loop. The radius of the vertical loop is 12.5 cm. At the top of the loop, the magnitude of the gravitational force is 1.25 times the magnitude of the normal force. Find the magnitude of the marble's velocity at the top.

A student created a device that rotated a 25-gram sphere attached to a cord in a 45-cm-radius vertical circular motion. At its highest position, the sphere's speed is 2.5 m/s, and at its lowest position, it is 5.6 m/s. Calculate the gravitational force on the sphere at the highest and lowest points and write your answer in unit vector notation.

An object of mass 0.125 kg attached to a cable revolves in a vertical circular motion of radius 0.5 m. The magnitude of the velocity is 4.5 m/s at the highest vertical position and 7.8 m/s at the lowest vertical position. Find the cable's tension at the highest vertical position.

For a science fair, a student attaches a marble of mass 250 g to the end of a metallic wire of length 1.15 m. The wire is suspended vertically from the free end on a frictionless pivot. The stretched wire and the marble are displaced by an angle θ and released. The system oscillates in a vertical plane. The marble's speed at the bottom of its motion is 6.3 m/s. Find the tension in the wire at the bottom.

During a washing cycle, the 40 cm diameter drum of a washing machine rotates about a horizontal axis. A child put her 300 g doll inside the washer. The rotation period of the drum is adjustable. Find the maximum rotation period of the drum that keeps the doll stuck to the drum at its highest position.

A tiny sphere of mass 125 g revolves in a vertical plane around a horizontal axis at the end of a cable of length 80 cm. What should be the minimum angular acceleration of rotation in order for the sphere to complete a full revolution without the cable becoming loose at the highest position?

A motion capture system is employed to track the motion of an adult pedestrian walking over a rigid, level surface. The position of the center of gravity of the pedestrian is investigated. According to the data analysis, the pedestrian's center of gravity follows a vertically curved (circular) path when walking. Furthermore, the center of gravity is defined by an arc with a radius of 1.0 m. Determine the minimum speed at which a pedestrian starts to run.

A bird that can withstand an acceleration of 11g sees its prey during flight. It dives vertically down to catch it at a constant speed of 350 m/s. At what height above the ground the bird must begin to pull out (following a vertical circular trajectory) to avoid blacking out and crashing into the ground.

A low-flying jet plane performs a loop-the-loop in such a way that at the topmost point of the loop, the jet is upside down. Inside the jet, the pilot has forgotten to fasten her seatbelt. Given that, the radius of the loop is 5.5 m determine what the minimum speed of the jet plane should be so that the pilot does not fall out of her seat at the topmost point of the loop. 

Scientists are experimenting on a mouse kept inside a 'ring torus' like structure that is in space, as shown in the figure. The structure rotates about its center. Given the outer diameter of the structure to be 0.40 km, calculate its rotation speed in revolutions per day if an artificial gravity-like effect, which is almost equal to that on Earth, 0.88 g, is to be simulated for the mouse inside. Suggest where they should place the mouse.

A roller coaster includes a vertical loop that provides thrilling experiences to its riders. As shown below, the loop has a radius of 15.0 meters and the coaster completes the loop in 6.0 seconds. Find the ratio of a passenger's apparent weight to their real weight at the bottom of the loop.