Answers to some Ch 1 and 2 Questions
When a car hits a tree the forces exerted by car on tree and by tree on car are equal and opposite. The structure of a large tree is stronger than that of a car, so the force does more damage to the car than to the tree. If a less massive object collides with a more massive object, they exert equal and opposite forces on one another, but the magnitude of a = F_net / m is greater for the less massive object (smaller denominator implies greater result). The duration of the force is the same for one object as for the other, so the less massive object will change speed by more.
If a domino has a weight of .18 N +- .05 N then the error as a proportion of the weight is is .05 N / 1.8 N = .03, which is expressed as a percent is about a 3%.
The acceleration of gravity is the acceleration of an object in free fall, which near the surface of the Earth is 9.8 m/s^2 or 980 cm/s^2, expressed to 2 significant figures. For an object in free fall, its v vs. t graph will therefore have slope 9.8 m/s^2 or 980 cm/s^2.
If an object traveling initially in the horizontal direction at 25 cm/s falls 90 cm to the floor, then its initial vertical velocity is 0, its acceleration in the vertical direction is 980 cm/s^2 downward and its vertical displacement is 90 cm downward.
A ball rolling down a ramp converts its gravitational potential energy at the top of the ramp into translational kinetic energy, resulting in its final velocity, as well as into rotational kinetic energy (it takes energy to get it spinning and it's spinning when it comes off the ramp). So it's not moving as fast as it would if there was no friction to help create the spin. A person diving off a board can dive with minimal rotation, in which case their center of mass will be moving faster just after the leave the board, or can convert some energy into spin, in which case (all other factors being equal) their center of mass will not be moving as fast.
Gravitational force is not 9.80 m/s^2. That is the acceleration of gravity in the vicinity of the Earth's surface. Gravitational force is obtained using Newton's Second Law, multiplying mass by gravitational acceleration.
If uncertainty is .001 on a quantity with magnitude .185 then the proportional uncertainty is .001 / .185 = .0054, approx., which is about .54%. This means that the uncertainty is about .54% of the quantity being measured.
Question: "Does the length of a pendulum affect the period more than the mass of the weight?". The mass of the pendulum has no effect on its period. At any point the net force is a certain portion of its weight (this proportion depends on the length of the pendulum and the pullback displacement), so the net force on a greater mass is proportionally greater. Thus for a given length and pullback distance, F_net and m are both proportional to the mass of the pendulum, and when we divide F by m we get the same thing regardless of the mass.
There is a question about the acceleration of an object slowing down and if it is constant or not. The answer depends on the details, and the details were not given. However acceleration is rate of change of velocity with respect to clock time, average acceleration over an interval is `dv / `dt, and acceleration is represented by the slope of a graph of v vs. t. Depending on the given information, you would likely use one of these techniques to determine whether acceleration is constant.
Percent uncertainty is uncertainty / quantity, expressed as a percent.
Question: What is the definition of rate of change. Answer: See the definition of rate of change of A with respect to B. That's it.
A student says he/she is having trouble applying Newton's Second Law to text problems and examples. More specific details would be useful, and a question should include what you do and do not understand. However in the scheme of things, a = F_net / m so if you know any two of the quantities F_net, m and a you can find the third. If F_net and m are known to be constant, you can also use the analysis of uniformly accelerated motion (e.g., calculate a = F_net / m then use this acceleration in your analysis of motion). Or if you can find the acceleration by analyzing motion, you can then use knowledge of F_net to find m, or m to find F_net.
If you speed up too fast the cup on your car's seat might appear to you to accelerate backwards. From the point of someone standing by the roadside, your car accelerates in the forward direction, as does your cup. But the cup's acceleration is less than that of the car, so at any instant while this is the case the car moves faster than the cup. The cup continues to 'lose ground' to the car until it hits the back of the seat.
If you are given initial and final velocities, and the information that the object has rolled off a vertical cliff, then the object is in free fall and you know its acceleration to be 9.8 m/s^2 or 980 cm/s^2. So you know v0, vf and a. You could solve using the equations of motion, or you could reason out the solution. Reasoning: a = `dv / `dt and you know `dv = vf - v0, so you can find `dt. From vf and v0 you can also find vAve (sketch your v vs. t graph as an aid so you can see why vAve = (vf + v0) / 2 rather than vf - v0, or vf - v0 / 2, neither of which make any sense in terms of words or the graph), and once you know vAve you use `dt to find `ds.
Question: How do you figure out the suction force required to pull a car out of the mud? Answer: From just this information you can't. Include all relevant information in your question, including what you do and do not understand about the situation and the possible relationships you might consider in order to solve it.
Question: A car is drifting down a slope and the velocity is positive and increase, acceleration negative and becoming more negative. Is it correct to say that the average slope of the hill is greatest when the velocity is the highest and the acceleration is the most negative? Answer: The slope of the hill determines the acceleration (i.e., the gravitational component of the weight in the direction parallel to motion). The slope of the hill at a point is unrelated to the velocity of the car at that point; the velocity depends on the shape of the entire hill and the car's velocity at the initial point, so the slope at a point tells you nothing about the velocity at that point. The slope is relevant only to the rate of change of the velocity.