Practice problems for the 2nd exam

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1 Practice problems for the 2nd exam Show your work and the solutions so the instructor can see how much you put efforts to understand. This will be one of your credits toward your final grade. 1. A 4.60-kg sled is pulled across a smooth ice surface (non-inclined). The force acting on the sled is of magnitude 6.20 N and points in a direction 35.0 o above the horizontal. If the sled starts at rest, how fast is it going after being pulled for 1.15 s? [Conceptual note: Can you obtain the free-body diagram? What if the surface is not smooth?] 2. The coefficient of static friction is between the object and surface as shown. The object starts to move by a 4.50-N force. Find the mass of the object. [Conceptual note: How does the freebody diagram look like?] 3. The weight of an object on the planet, Neptune, is found as 62.0 N. Find the mass of the object knowing that the gravitational acceleration on the Neptune is 13.3 m/s 2. [Conceptual note: Then, can you find the weight on the Earth?] 4. Find the normal force when you push down the object as shown. The magnitude of the force vector shown is 16.0 N, and the angle, θ, is 35.0 o. The mass of the object on the table is 3.02 kg. [Conceptual note: How about if the angle given is measured from the vertical?] 5. Two objects are connected by a cord as shown. Draw the force vectors, and set up the equations of motion for the motional and its perpendicular axes. The coefficient of kinetic friction between the block and table is µ k. (Do not solve the equations.) [Conceptual note: Do you remember the procedure to derive the equations of motion?] M m 6. An object (the mass = m) slides down on the inclined surface. Draw the force vectors on the object shown; set up the equations of motion for two axes; and then solve for the acceleration, knowing that θ and µ k are 35 o and 0.20, respectively. [Conceptual note: Note that drawing the magnitude of each vector is also important. What if there is no friction?]

2 7. There is a spring and hung vertically from ceiling. If you hang a 1.72-kg mass to the spring, the spring is elongated by m. What is the spring constant? [Conceptual note: Do you know the name of this law?] 8. A ship propelled by a 21.0-N force. Due to the force, the energy per unit time is 4,600 W. Find the velocity of the ship. [Conceptual note: What is the name of the physical quantity of energy per unit time?] 9. The work done by the force shown is 5.30 J. The magnitude of the force and the displacement are 3.15 N and 8.28 m, respectively. Find the angle shown in the figure. [Conceptual note: How about if the angle is given from the horizontal?] 10. A ball revolves on a circular track with 5.0 times per second. Knowing the speed of the ball as 3.2 m/s, find the radius of the track. [Conceptual note: What is the difference between frequency and period?] 11. Use the conservation of energy. If you drop a 1.20-kg object from 5.60-m height. Find the velocity at 2.20-m height? [Conceptual note: What if the potential energy is different, such as spring?] 12. An 82.0-kg mountain climber is in the final stage of ascent of 4301-m-high Pikes Peak. What is the change in gravitational potential energy as the climber gains the last m of altitude? (Let PE = 0 be at sea level.) [Conceptual note: Does this depend on the height of mountains?] 13. With a uniform circular motion, the acceleration directed to the center of the motion is found as 0.85 m/s 2. The radius of the circle is 0.51 m. Find the time for one cycle of this motion. [Conceptual note: Can you also find how many times it revolves per second?]

3 14. Calculate the amount of power to lift an 80-kg box vertically upward at a uniform speed of 0.45 m/s. [Conceptual note: Can you calculate the total energy if it takes 30 seconds to lift at certain level?] 15. A spring, whose spring constant is 6.05 N/m, is hanged from ceiling with a kg object. If it is stretched from the equilibrium position by m, what is the maximum speed of the motion after releasing it? [Conceptual note: Can you describe the difference between force and energy with a spring?] 16. There are two planets, whose masses are kg and kg. The distance between them is m. Knowing that the universal gravitation constant is N m 2 /kg 2, find the gravitational force between these planets. [Conceptual note: In principle, any object having mass experiences a gravitational force from the other mass.] 17. Find the minimum angle at which the roadbed has to be banked so that your car driving at 20.0 m/s can securely negotiate the curve. The radius of the curve is m. [Conceptual note: Do you know that the horizontal component of the normal force is responsible for holding the car in this frictionless banked curve?] 18. A 1000-kg car travels at 14.0 m/s. How much work is needed to stop the car in 10 seconds? [Conceptual note: What is the relationship between work and kinetic energy?] 19. A kg glass of water is slid on a horizontal surface. The initial speed is m/s. If the glass comes to rest with constant acceleration in m/s 2, what is the coefficient of kinetic friction between the glass and the table? Use Newton s equation of motion to solve this. [Conceptual note: Can you also look at this with a perspective from the work-energy theorem?]

4 20. The mass of the object is kg. The initial velocity is m/s. At the final point, the object stops. Knowing that the coefficient kinetic friction is 0.038, find the distance the object travels by using the Work-Energy theorem. [Conceptual note: Can you also look at this with a perspective from Newton s equation of motion?] 21. The mass of the spacecraft is kg and the mass of astronaut is 92 kg. The astronaut exerts a force of +36 N on the spacecraft. Find the acceleration of the astronaut. (Assume that there is no gravity.) [Conceptual note: How about the acceleration of the spacecraft?] 22. There is a planet. The size is three times as large as that of the Earth. The mass is twice as large as that of the Earth. Find the gravitational acceleration of the planet. [Conceptual note: How does the gravitational acceleration depend on the mass and the radius of a planet?] 23. Find the resultant force of the two forces pulling the wall as shown in the figure. The magnitude of each force is 23.0 N and the angle θ is 17.0 o. [Conceptual note: When the block hanged from a ceiling by two ropes with different angles, can you solve the problem?] 24. An object (0.25 kg) attached to a string is rotating in a horizontal circle uniformly. The radius of the motion is 0.50 m. Knowing that it revolves twice a second, what is the tension in the string? [Conceptual note: What is the definition of frequency? Do you notice that this tension is equivalent with centripetal force?] 25. An ice cube is placed in a microwave oven. Suppose the oven delivers 255 W of power to the ice cube and that it takes 47.0 s to melt it. What is the total energy to take for the ice cube to melt? [Conceptual note: What is the relationship between power and energy?]

5 26. A motorcycle driver goes into a vertical loop as shown with a uniform speed. Find the minimum speed to go through the top of the loop and the normal force at the bottom with that speed. The total mass of the driver and the motorcycle is 197 kg. The radius of the loop is 12.8 m. [Conceptual note: What is the condition the driver feels weightlessness at the top?] Check out the following before taking the exam: Can you solve all the questions from the beginning without any help and hints? Do you understand the concept behind each question? Can you relate each question to the lecture topics? Can you visualize the physical situation of each problem? Answer Keys m/s kg kg N 5. Object hanged : motional-axis ΣF=mg-T=ma Object on the plane: motional-axis ΣF=T-µ k n=ma; perp. to motional-axis: ΣF=n-Mg=0 6. Along the slope: ΣF=mgsinθ-µ k n=ma perpendicular to the slope: ΣF=n-mgcosθ=0 4.0 m/s N/m m/s o m m/s J s W m/s N o J m m/s /9g E or 2.18 m/s N N J m/s; 3860 N

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