# Physics equations/06-Uniform Circular Motion and Gravitation/UPTA STEM

1.(Centripetal force, banked surface: Knight 2nd edition page 231 #8). A highway curve of radius 500 m is designed for traffic moving at 90 km/hr. What is the correct banking angle of the road?

2.(Centripetal force, unbanked surface: Knight 2nd edition page 231 #5). A 1500 kg car takes a 50-m-radius unbanked curve at 15 m/s. What is the size of the friction force on the car?

3.(Centripetal force, looped surface: Knight 2nd edition page 233 #41). In an amusement park ride called the Roundup, passengers stand inside a 16-m-diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure.

a)Suppose the ring rotates once every 4.5 s. If a rider’s mass is 55 kg, with how much force does the ring push on her at the top of the ride? At the bottom?

b)What is the longest rotational period of the wheel that will prevent the riders from falling off at the top?

4.(Centripetal force, tension in a cord, horizontal plane: Serway 7th edition page 159 #50). An air puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless horizontal table. The other end of the string passes through a small hole in the center of the table, and a load of mass m2 is tied to the string, as shown in the figure. The suspended load remains in equilibrium while the puck on the tabletop revolves.

a)What is the tension in the string?

b)What is the radial force acting on the puck?

c)What is the speed of the puck?

d)Qualitatively describe what will happen in the motion of the puck if the value of m2 is somewhat increased by placing an additional load on it.

e)Qualitatively describe what will happen in the motion of the puck if the value of m2 is instead decreased by removing a part of the hanging load.

5.(Centripetal force, tension in a cord, at angle to horizontal plane: Serway 7th edition page 160 #53). An amusement park ride consists of a rotating circular platform 8.00 m in diameter from which 10.0-kg seats are suspended at the end of 2.50-m massless chains, as shown in the figure. When the system rotates, the chains make an angle θ = 28.0° with the vertical.

a)What is the speed of each seat?

b)Draw a free-body diagram of a 40.0-kg child riding in a seat and find the tension in the chain.

6.(Centripetal acceleration, conceptual: Knight 2nd edition page 230 #3). The following figure is a bird’s eye view of particles moving in horizontal circles on a tabletop (scan and insert figure). All are moving at the same speed.

a)Rank in order, from largest to smallest, the tensions Ta to Td. Give your answer in the form a > b = c > d and explain your ranking.

b)Calculate the angular speeds ωa, ωb, ωc, and ωd.

7(Rotational kinematics with constant acceleration: Serway 7th edition page 300 #6). A rotating wheel requires 3.00 s to rotate through 37.0 revolutions. Its angular speed at the end of the 3.00-s interval is 98.0 rad/s. What is the constant angular acceleration of the wheel?

8.(Multi-curve problem: Serway 7th edition page 156 #14). A roller-coaster car (see figure below) has a mass of 500 kg when fully loaded with passengers.

a)If the vehicle has a speed of 20.0 m/s at point A , what is the force exerted by the track on the car at this point?

b)What is the maximum speed the vehicle can have at point B and still remain on the track?