Physics 1307 Practice Quiz Chapters 23
Physics 1307 Practice Quiz Chapters 23
Problems 1. Describe, using graphs, the motion of a particle that moves with constant acceleration equal to 9.8m/s² and starts with velocity equal to 10 m/s from the origin. 2. A car traveling at constant speed of 45 m/s passes a trooper on a motorcycle hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch the car, accelerating at constant rate of 3.00 m/s². How long does it take her to overtake the car? Problem Solving 1. 2. 3. 4. 5.
Read and reread the whole problem carefully before trying to solve it. Draw a diagram or picture of the situation, with coordinate axes wherever applicable. Write down what quantities are known or given and then what you want to know. Think about which principles or physics apply to the particular problem. Consider which equations (and/or definitions) relate the quantities involved. Before using them, be sure their range of validity includes your problem. 6. Carry out the calculation if it is a numerical problem. Keep one or two extra digits during the calculations, but round off the final answers to the correct number of significant figures. 7. Think carefully about the result you obtain: Is it reasonable? Does it make sense according to your own intuition and experience? 8. A very important aspect of doing problems is keeping track of units. Note that an equals sign implies the units on each side must be the same, just as the numbers must. If the units do not balance, a mistake has been made. Always use a consistent set of units.
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Solutions 1. Let us first draw a diagram with the information provided. I am going to assume that the positive direction is up the page and therefore the negative direction is down the page: a a= 9.8 m/s² + t 9.8 Vi=10 m/s
Since the acceleration is constant and negative we have a straight line on the negative axis on the a vs t diagram. Now we observe that the initial velocity and the acceleration point in opposite directions. This implies that with enough time the velocity will reach zero magnitude and invert its direction and become parallel to the acceleration. The v vs t diagram should look something like the left hand side graph: v
x
10
t1/2 t1/2
t
t
Note that at t = 0 s the velocity is equal to 10m/s as it is given in the problem and the line describing the velocity crosses the taxis. At this point the velocity is zero (in this problem the acceleration is always different from zero) and after this, the velocity becomes negative, i.e. the object moves towards the origin. Thus the position vs time diagram reflects this pattern: the object first moves away from the origin and, after t1/2 , moves back toward the origin, i.e reaches again x = 0.
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2. Let us define the billboard as origin of the reference frame and time zero as the instant when the cop begins the chase. Since the car moves with constant velocity and the motorcycle moves with constant acceleration a graph showing both motions will look something like the diagram below (it is easy to figure out what each line is representing) : Now our job is to find ti the time when both lines intersect. This is equivalent to the following equality: x d =x c
x
45 ti
1 v d t i45= a t i2 2 which can be rewritten as quadratic equation: t m m 0=1.5 2 t i2 −45.0 t i−45.0 m s s solving this relation and using (why?) the positive solution one obtains ti= 30 s.
Observe that 45 m is the distance that the car has covered in the first second, i.e the distance that the speeding driver has covered before the trooper starts her chase.
3/3
Problems 1. Describe, using graphs, the motion of a particle that moves with constant acceleration equal to 9.8m/s² and starts with velocity equal to 10 m/s from the origin. 2. A car traveling at constant speed of 45 m/s passes a trooper on a motorcycle hidden behind a billboard. One second after the speeding car passes the billboard, the trooper sets out from the billboard to catch the car, accelerating at constant rate of 3.00 m/s². How long does it take her to overtake the car? Problem Solving 1. 2. 3. 4. 5.
Read and reread the whole problem carefully before trying to solve it. Draw a diagram or picture of the situation, with coordinate axes wherever applicable. Write down what quantities are known or given and then what you want to know. Think about which principles or physics apply to the particular problem. Consider which equations (and/or definitions) relate the quantities involved. Before using them, be sure their range of validity includes your problem. 6. Carry out the calculation if it is a numerical problem. Keep one or two extra digits during the calculations, but round off the final answers to the correct number of significant figures. 7. Think carefully about the result you obtain: Is it reasonable? Does it make sense according to your own intuition and experience? 8. A very important aspect of doing problems is keeping track of units. Note that an equals sign implies the units on each side must be the same, just as the numbers must. If the units do not balance, a mistake has been made. Always use a consistent set of units.
1/3
Solutions 1. Let us first draw a diagram with the information provided. I am going to assume that the positive direction is up the page and therefore the negative direction is down the page: a a= 9.8 m/s² + t 9.8 Vi=10 m/s
Since the acceleration is constant and negative we have a straight line on the negative axis on the a vs t diagram. Now we observe that the initial velocity and the acceleration point in opposite directions. This implies that with enough time the velocity will reach zero magnitude and invert its direction and become parallel to the acceleration. The v vs t diagram should look something like the left hand side graph: v
x
10
t1/2 t1/2
t
t
Note that at t = 0 s the velocity is equal to 10m/s as it is given in the problem and the line describing the velocity crosses the taxis. At this point the velocity is zero (in this problem the acceleration is always different from zero) and after this, the velocity becomes negative, i.e. the object moves towards the origin. Thus the position vs time diagram reflects this pattern: the object first moves away from the origin and, after t1/2 , moves back toward the origin, i.e reaches again x = 0.
2/3
2. Let us define the billboard as origin of the reference frame and time zero as the instant when the cop begins the chase. Since the car moves with constant velocity and the motorcycle moves with constant acceleration a graph showing both motions will look something like the diagram below (it is easy to figure out what each line is representing) : Now our job is to find ti the time when both lines intersect. This is equivalent to the following equality: x d =x c
x
45 ti
1 v d t i45= a t i2 2 which can be rewritten as quadratic equation: t m m 0=1.5 2 t i2 −45.0 t i−45.0 m s s solving this relation and using (why?) the positive solution one obtains ti= 30 s.
Observe that 45 m is the distance that the car has covered in the first second, i.e the distance that the speeding driver has covered before the trooper starts her chase.
3/3
