Physics 211 Test 2 Practice August 31, 2011

Transcription

1 Multiple choice questions 2 points each. Physics 211 Test 2 Practice August 31, Suppose several forces are acting on a mass m. The F in F = m a refers to (a) any particular one of the forces. (b) the vector sum of all the forces. (c) the force of friction acting upon the mass. (d) the arithmetic sum of all the forces. (e) the arithmetic mean of all the forces. 2. A 4 kg mass moving with a speed 2m/s, and a 2kg mass moving with a speed of 4m/s, are gliding over a horizontal frictionless surface. Both objects encounter the same horizontal force, which directly opposes their motion, and are brought to rest by it. Which statement correctly describes the situation? (a) Both masses travel the same distance before stopping. (b) the 2-kg mass travels twice as far as the 4-kg mass before stopping. (c) the 2-kg mass travels farther, but not necessarily twice as far. (d) the 4-kg mass travels twice as far as the 2-kg mass before stopping. (e) the 4-kg mass losses more kinetic energy than the 2-kg mass. 3. Consider two unequal masses, M and m. Which of the following statements is false? (a) It is possible for the center of mass to lie within one of the objects. (b) The center of mass is closer to the larger mass. (c) The center of mass lies on the line joining the centers of each mass. (d) If a uniform rod of mass m were to join the two masses, this would not alter the position of the center of mass of the system without the rod present. 4. In an elastic collision, the final total momentum is (a) more than the initial momentum. (b) less than the initial momentum. (c) the same as the initial momentum. (d) insufficient information to answer. C W Fay IV: Spring2011 1

2 5. You and your friend want to go to the top of the eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy (U) of you and your friend, after you both reach the top, assuming that you and your friend have equal masses. (a) It is impossible to tell, since the times and the distances are unknown. (b) Your friend s U is greater than your U, because she got to the top faster. (c) Both of you have the same amount of potiential energy. (d) Your U is greater than your friend s U, because you traveled a greater distance in getting to the top. 6. (5 points) An auto is costing on a level road. It weighs 10.kN. How much work is done by gravity as it moves horizontally 150. meters? Solution: No work is done as the force and the movement are perpendicular. 7. (5 points) Describe mechanical efficiency. Solution: The efficency is the ratio of the work derived from a system over the energy put into a system. 8. (15 points) To get off a frozen, frictionless lake, a 68.0kg person takes off a 0.100kg shoe and throws it horizontally, directly away from the shore with a speed of 2.00m/s. If the person is 5.00m from the shore, how long does he take to reach it? Given: m m = 68.0kg m s = 0.100kg v s = 2.00m/s x = 5.00m t =? Using the conservation of momentum, p i = p f (1) 0 = p man p shoe (2) p man = p shoe (3) m 1 v m = m s v s (4) v m = m sv s m m = m/s (5) since there is no acceleration in the x-direction (frictionless) Given: a x = 0m/s 2 v 0 = v m (6) x = x 0 + v 0 t + 1/2a x t 2 (7) x = v 0 t (8) t = x v m (9) = m m x = s m s v s (10) 9. (5 points) A 10g bullet moving horizontally at 400m/s penetrates a 3.0kg wood block resting on a horizontal surface. If the bullet slows down to 300m/s after emerging from the block, what is the speed of the block immediately after the bullet emerges? C W Fay IV: Spring2011 2

3 v =? Solution: Given: m 1 = 10g m 2 = 3.0kg v 1 = 400m/s v 1f = 300m/s p 1 = p 2 (11) m 1 v 1 = m 1 v 1f + m 2 v 2f (12) v 2f = m 1v 1 m 1 v 1f m 2 = 0.33m/s (13) 10. A 5.0kg block sits on an plane with a rough surface that is inclined at 30. (a) (5 points) Draw a free-body diagram for the block. (b) (10 points) if the block is in equilibrium, what is coefficient of static friction? µ s = Solution given: m = 5.0kg θ = 30 use Newton s second law and the first condition of equilibrium (a = 0m/s 2 ) F = mg sin θ f = 0 (14) F = F N mg cos θ = 0 (15) f = mg sin θ (16) F N = mg cos θ (17) f = µf N = µmg cos θ = mg sin θ (18) µ = mg sin θ = tan θ = 0.58 mg cos θ (19) 11. A collision occurs between a mass of m 1 = 1.00kg and a mass m 2 = 2.00kg, before the collision the masses have velocities of v 10 = 2.00m/s 2 and v 20 = 0.500m/s 2, if after the collision the first mass has a velocity of v 1 = 1.00m/s 2. (a) (10 points) After the collision, what is the final velocity of the second mass? v 2 = (b) (5 points) Is this collision perfectly elastic? Why or why not? given: m 1 = 1.00kg v 1 = 1.00m/s 2 m 2 = 2.00kg v 10 = 2.00m/s 2 v 20 = 0.500m/s 2 a) m 1 v 10 + m 2 v 20 = m 1 v 1 + m 2 v 2 (20) v 2 = m 1 m 2 (v 10 v 1 ) + v 20 (21) v 2 = 1 (2 ( 1)) + ( 0.5) = 1.00m/s (22) 2 C W Fay IV: Spring2011 3

4 b) We have to answer is energy conserved? E i = 1 2 m 1v m 2v 2 20 = 2.25J (23) E f = 1 2 m 1v m 2v 2 2 = 1.5J (24) No energy is not conserved, so the collision is not perfectly elastic. 12. A 20.0g ball falls on a table, If the initial velocity of the ball is 3.00m/s and after it hits the table it has a velocity of 2.50m/s upward. The ball is in contact with the table for s. (a) (10 Points) what is the force on the table? F = (b) (5 Points) What is the efficiency of this process? ε = Solution: Given: m = 20.0kg v 0 = 3.00m/s v f = 2.50m/s t = s (a) what is the force on the table? F = F = ma = m v t = (0.020kg)( 3.00m/s) (2.50m/s) s = 110N (25) (b) (extra credit) What is the efficiency of this process? ε = ε = W out E in = K E in (26) W out = 1 2 mv2 2 0 (27) E in = 1 2 mv2 1 (28) ε = 1 2 mv mv2 1 = v2 2 v 2 1 =.694 = 69.4% (29) 13. (10 points) A ball of mass 0.500kg is thrown vertically with velocity 20.0m/s. what is the potential energy after the speed has dropped to half of its initial value? U =? The potential energy when the speed has dropped by half is given by the total energy minusthe new kinetic energy, U = E T 1 2 m(v 2 )2 = 1 2 mv2 1 2 m(v 2 )2 = 3 8 mv2 (30) = 3 8 (0.500kg)(20.0m/s)2 = 75J (31) 14. (5 points) A loaded Boeing 747 jumbo jet has a mass of kg. What net force is required to give the plane an acceleration of 4.0m/s 2 down the runway for takeoff? C W Fay IV: Spring2011 4

5 F = given: m = kg a = 4.0m/s 2 F = ma = N (32) C W Fay IV: Spring2011 5