PROBLEMS
1. A bee strikes a windshield of a car on the freeway and gets crushed. What can you conclude about the force on the bee versus the force on the windshield, and on what principle is this based?
2. A car is traveling at top speed on the Bonneville salt flats while attempting a land speed record. The tires exert 25 kN of force in the backward direction on the ground. Why backwards? How large are the forces resisting the forward motion of the car, and why?
3. A sky diver of mass 90 kg (with suit and gear) is falling at terminal speed. What is the upward force of air drag, and how do you know?
4. A cart on wheels (assume frictionless) with a mass of 20 kg is pulled rightward with a 50N force. What is its acceleration?
5. What will the acceleration be in the previous problem if the wheels effectively give the cart a coefficient of friction of
6. In the previous problem, the rightward pull is now directed at an angle of 30 degrees upward from horizontal while the cart still rolls horizontally. What is the cart's acceleration?
7. Using Newton's 2nd law, show that all objects subject to the pull of gravity alone should fall at the same rate. What is that rate?
8. What is the third law pair to the normal force as you sit in a chair? What effect does the sun's pull on earth have in terms of third law pairs?
9. Two planets, each of mass 1020kg are at coordinates and Find the force on each planet by the other.
10. A hydrogen atom has just a single electron orbiting the nucleus, which happens to be a single proton without any neutrons. The proton is positively charged, the electron negatively, but both with the same magnitude of charge given by e=1.602x10-19C. The mass of an electron is 9.11x10-31kg, and the proton is 1.67x10-27kg. Find the ratio of the electrostatic to the gravitational force of attraction between the electron and the proton in hydrogen.
11. What is the meaning of a first order approximation?
12. What is a good general rule to follow in order to find the best choice of coordinate system to solve a dynamics problem?
13. A box with friction coefficient of 0.2 rests on a 12 foot long plank of wood. How high (in feet) must one side of the plank be lifted in order for the box to begin to slide?
14. A skateboarder starts from rest and rolls down a 3.0 m long 5% ramp, and then rolls up another 5% ramp. How far will they make it up the second ramp if
a) there is zero friction?
b) there is a friction coefficient of 0.01?
Please do this problem using kinematics and not energy (which you should only know from a previous course, since we have not yet arrived at that topic).
15. A toy car speeds up at 1.0 m/s2 while rolling down a ramp, and slows down at a rate of 2.0 m/s2 while rolling up the same ramp. What is the slope of the ramp in degrees? Grade in %?
16. A crate rests on the back of a flat-bed semi truck that is driving at 20 m/s. The crate is dangerously not strapped down. What is the shortest stopping distance possible for the truck such that the crate does not slide on the truck bed if the friction coefficient between the crate and the bed of the truck is 0.40?
17. A box is dropped on a level conveyor belt that is moving at 4.5 m/s in the +x direction in a shipping facility. The box/belt friction coefficient is 0.15. For what duration will the box slide on the belt? In which direction does the friction force act on the box? How far will the box have moved horizontally by the time it stops sliding along the belt?
18. A little toy car is powered by a CO2 cartridge that produces a thrust force according to the following function: Fthrust(t) = 6.0N e-0.2t. The car also has a friction coefficient of 0.05 due to the wheels and bearings. If the car's mass is 1.2kg, and the car travels in the +x direction, what will it's acceleration function look like as a function of time? If it starts from rest, what will vx(t) be? How fast will the car be going after 3.0s? What maximum speed will be reached by the car?
19. A rocket's velocity (measured with respect to a nearby planet) changes from to
upon being struck by an asteroid. The asteroid's mass is 1/10th that of the rocket and upon impact got embedded into the sheet metal of the rocket rather than flying away. What was the asteroid's incoming velocity as measured with respect to the same nearby planet?
20. Two objects get pushed by the same magnitude of force. One object is 10x more massive. How does the rate of change of momentum for the more massive object compare with the less massive one? Please be able to explain why in terms of a quantitative statement found in the chapter.
ANSWERS
1. Read about third law.
2. 25 kN
3. 900 N
4. 2.5 m/s2
5. 1.5 m/s2
6. 1.3 m/s2
7. so
8. Read corresponding section.
9. and the opposite force for the other object.
10. 2.27x1039
11. See text
12. See text
13. 2.35 ft
14. 3.0m; 2.0m
15. 8.6o
16. 50m
17. 3s, to the right, 6.75m
18. a(t)=5e-0.2t-0.5, v(t)=25(1-e-0.2t)-0.5t, 9.8m/s, 16.7m/s
19.
20. It is the same.