26. For an object moving in uniform circular motion, the magnitude of the centripetal acceleration is given by 𝑎_𝑐 = 𝑣²/𝑟, where 𝑣 is the speed of the object, and 𝑟 is the radius of the circle. The “jerk” is the rate of change of acceleration. For uniform circular motion, the magnitude of the jerk is given by:

27. A machine gun fires 100 g bullets at a speed of 1000 m/s. The person holding the machine gun in their hands can exert an average force of 150 N against the gun. If the gun is to remain stationary, what is the maximum number of bullets that can be fired per minute?

28. A spring with spring constant k = 20 kN/m, is used to stop a 50 kg box that is sliding on a horizontal surface. The spring is initially in its equilibrium state. At position A, shown in the top diagram, the box has a speed of 3.0 m/s. The compression of the spring when the box is instantaneously at rest (position B in the bottom diagram) is 120 mm. Determine the coefficient of kinetic friction between the box and the surface.

 

30. A ticker tape timer is operating at 60 Hz. It was used to analyze the motion of a battery-powered car. The following displacements were measured for five intervals on the ticker tape.

 

 

What is the average speed of the car?

31. Water drips from the nozzle of a shower onto the floor 2.45 m below. The drops fall at regular intervals of time, the first drop striking the floor at the instant the third drop begins to fall. Measured from the shower head, what is the location of the second drop when the first drop strikes the floor.

32. A star initially has a radius of 6 x 10⁸ m and a period of rotation about its axis of 30 days. Eventually, it collapses to form a neutron star with a radius of only 1 x 10⁴ m and a period of 0.1 s. Assuming that the mass has not changed, find the ratio of initial and final angular momentum of the star.

35. A combination of two thin convex lenses is placed as shown below. An object is placed 5 cm in front of L₁ which has a focal length of 10 cm. L₂ is 10 cm behind L₁ and has a focal length of 12 cm. How far from L₂ is the final image for this lens combination?

 

37. A car and a truck are both traveling with a constant speed of 20 m/s. The car is 10 m behind the truck. The truck driver suddenly applies his brakes, causing the truck to slow to a stop at the constant rate of 2 m/s2. Two seconds later, the driver of the car applies their brakes and just manages to avoid a rear-end collision. Determine the constant rate at which the car slowed.

38. In the circuit shown below, the voltage source, switch, capacitor and connecting wires have no resistance. Let ΔVR and ΔVC represent the potential differences across the resistor and the capacitor, respectively. The capacitor is initially uncharged. Which of the following choices correctly compares these potential differences immediately after the switch is closed and after the circuit has reached steady state.

 

   

43. A triangular glass prism (n = 1.6) is immersed in a liquid (n = 1.1) as shown. A laser light is incident as shown on face AB making an angle of 20^o with the normal (N). Calculate the angle that the ray emerging from AC makes with the ground when it leaves AC and strikes the ground.

44. How long would it take 4.0 × 10²⁰ nuclei to decay to 1.0 × 10¹⁹ atoms if their half-life was 14.7 years?

46. Each of the two curved rods shown in the picture form one-quarter of a circle with a radius R. Both rods carry a uniformly-distributed electric charge +Q. Which of the following choices correctly expresses the net electric field and net electric potential at the origin? Assume V → 0 as r → ∞.

      

48. The diagram below shows combinations X, Y, and Z of three identical resistors. What is the correct order of the total resistance of the combinations going from lowest resistance to highest resistance?

 

49. If the Earth suddenly stopped in its orbit, and the orbit is assumed to be circular, how much time would elapse before it falls into the Sun?