Physics 18 Spring 2011 Homework 3 Wednesday February 2, 2011

Transcription

1 Physics 18 Spring 2011 Homework 3 Wednesday February 2, 2011 Make sure your name is on your homework, and please box your final answer. Because we will be giving partial credit, be sure to attempt all the problems, even if you don t finish them. The homework is due at the beginning of class on Wednesday, February 9th. Because the solutions will be posted immediately after class, no late homeworks can be accepted! You are welcome to ask questions during the discussion session or during office hours. 1. Astronauts in apparent weightlessness during their stay on the International Space Station must carefully monitor their masses because significant loss of body mass is known to cause serious medical problems. Give an example of how you might design equipment to measure the mass of an astronaut on the orbiting space station. 1

2 2. A net force of (6.0 N) î (3.0 N) ĵ acts on a 1.5 kg object. Find the acceleration a. What is the magnitude of the acceleration, a? 2

3 3. Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a crumple zone in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 m as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton s first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm. (a) A 60 kg person is in a head-on collusion. The car s speed at impact is 15 m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys. (b) Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag. (c) How do these two forces compare to the person s weight? 3

4 4. A 35.0-kg traffic light is supported by two wires as in the figure. (a) Draw the light s free-body diagram and use it to answer the following question qualitatively: Is the tension in wire 2 greater than or less than the tension in wire 1? (b) Verify your answer by applying Newton s laws and solving for the two tensions. 4

5 5. A 65-kg student weights himself by standing on a force scale mounted on a skateboard that is rolling down an incline, as shown in the figure. Assume there is no friction so that the force exerted by the incline on the skateboard is normal to the incline. What is the reading on the scale if θ = 30? 5

6 6. A block of mass m slides across a frictionless floor and then up a frictionless ramp. The angle of the ramp θ and the speed of the block before it starts up the ramp is v 0. The block will slide up to some height h above the floor before stopping. Show that h is independent of m and θ by deriving an expression for h in terms of v 0 and g. 6

7 7. A block of mass m is being lifted vertically by a uniform rope of mass M and length L. The rope is being pulled upward by a force applied to its top end, and the rope and block are accelerating upward with an acceleration of magnitude a. Show that the tension in the rope at a distance x (where x < L) above the block is given by (a + g) [m + (x/l) M]. 7

8 8. The figure shows a 20-kg block sliding on a 10-kg block. All surfaces are frictionless and the pulley is massless and frictionless. Find the acceleration of each block and the tension in the string that connects the blocks. 8

9 9. A 2.0 kg block rests on a frictionless wedge that has a 60 incline and an acceleration a to the right such that the mass remains stationary to the wedge. (a) Draw the free-body diagram of the block and use it to determine the magnitude of the acceleration. (b) What would happen if the wedge were given an acceleration larger than this value? Smaller than this value? 9

10 10. Elvis Presley has supposedly been sighted numerous times since his death on August 16, The following is a chart of what Elvis s weight would be if here were sighted on the surfaces of other objects in our solar system. Use the chart to determine: (a) Elvis s mass on Earth, (b) Elvis s mass on Pluto, and (c) the free-fall acceleration on Mars. (d) Compare the free-fall acceleration on Pluto to the free-fall acceleration on the moon. Planet Elvis s Weight (N) Mercury 431 Venus 1031 Earth 1133 Mars 431 Jupiter 2880 Saturn 1222 Pluto 58 Moon