12 calculus based physics questions

12 calculus based physics questions


1. A football player can launch the ball with a maximum initial velocity of 57 mph. What is the maximum height reached by the ball? Consider g = 9.80 m/s2 and 1 mile = 1.305 km. 15.3 m 21.8 33.1 325.2 m 36.29 2. An object moves by following a 2-dimensional curved path, as shown in the figure.   Which of the following is not true? The speed of the object can be constant. If the object moves with constant speed, then its acceleration has constant magnitude. The velocity  of the object cannot be constant. The acceleration  of the object cannot be constant. Such motion requires a net force acting on the object at all times. 3. Consider that the system of pulleys and masses shown in the schematic below is in equilibrium.   What is the relationship between masses m1 and m2? 3m1 =2m2 2m1=3m2 m1 = 6m2 6m1=m2 m1=3m2 m1=m2 4. Consider that the system of pulleys and masses shown in the schematic below is in equilibrium.   If m1=3kg what is the tension in point E? Consider g=10 m/s2. 20 N 30 N 40 N 60 N 5. Which of the following changes cannot increase the range of a projectile? Consider that friction is negligible. Increasing initial speed. Increasing launch angle. Decreasing launch angle. Increasing mass of the projectile. Increasing the vertical coordinate of the initial (launching) position. None of the above. 6. The rotor of a watermill consists of six identical slabs (each slab has mass M, width a, and length b) glued along the shorter edge b, as shown in the figure.   The moment of inertia of the rotor is closest to: Ma2 2Ma2 (1/2)Ma2 3Ma2 7. Three wheels are connected by a lightweight belt. The angular velocity for one wheel as well as radius and mass of all wheels are indicated in the figure.   What is the kinetic energy of the system? Consider that the wheels are equivalent with a thin-wall cylinder and the belt is tight (no slipping). 0.27 J 1.22 J 8.40 J 21.3 J 25.7 J 8. A force  applied at an angle α with the horizontal plane keeps a m = 100 kg uniform beam in equilibrium, as shown in the figure.   What is the angle α if the magnitude of F is three times the beam’s weight? 3.7° 9.6° 11.5° 14.5° 30° 45° 60° 9. An airplane has two fuel tanks located symmetrically in the wings, (see figure). As the airplane consumes fuel in equal amounts from the two tanks, its center of gravity shifts:   toward the back of the airplane. toward the front of the airplane. doesn’t change since equal amount of fuel is spent. cannot determine, additional information is needed. 10. A catapult sends projectiles with the same initial speed. A baseball followed by a basketball are each launched by the catapult so that the angle between the initial velocity vector and the horizontal decreases, θbaseball > θbasketball. Which projectile will land further? Consider that air friction is negligible. baseball basketball. baseball and basketball will land at the same distance from the catapult. all of the above cases are possible. 11. Two objects of mass m1 = 2m2 = 20kg are attached to a pulley via a heavy rope of mass m = 1.0kg and length L = 5.0 m, as shown in the figure. What is the work done by gravity as m1 pulls m2 all the way to the top (so it travels L/2 upward)?   Consider g=10 m/s2 , ignore friction, and consider that pulley’s mass and rotation have negligible impact. 0.407 J 22.1 J 262.5 J 430.8 J 2.06 J 12. A 5.0 kg object is subject to a variable horizontal force given by   where a = 0.5 N, b = 2 * 10-3 N/s, and c = 4 * 10-9  N/s2. How fast will the object move if the pull force is applied for 2 minutes? Consider that friction is negligible and initially the object was moving with v0=1.5 m/s. 1.7 m/s 13.4 m/s 14.9 m/s 16.4 m/s 18.2 m/s 40.1 m/s 41.6 m/s