PHYS 101 PHYSICS FOR ENGINEERS PLATE NO. 1 MOTION ALONG A STRAIGHT LINE Instruction 1: THE FOLLOWING PROBLEMS MAY REQUIRE YOU TO USE YOUR STUDENT NUMBER. PLEASE REMEMBER THE FOLLOWING FORMAT: ****-abcde e.g.: Student Number 2021-00345 means a=0, b=1, c=3, d=4, e=5. If the problem states that the height of the vessel is 1abc mm, it means 1013 mm. Additional Instruction 2: - Round off your final answer to two-decimal places (e.g. 6543.12, 543.12, 43.12). - For very small final answers, round off to at-least 4-significant figures (e.g. 1.234, 0.1234, 0.001234, 0.0001234) - Kindly, box your answer. Additional Instruction 3: - Don't forget to write your School Identification Number in your plates, otherwise your plates will not be checked. - The template provided on you, use the template sheet as your solution sheet. Every problem will be written in one template sheet. Note: Not following instructions will be deducted with 1 percent in each item. Late submission will be accepted before the term exam provided that the perfect score is 75 percent. Problem 1: While driving a car at 9e km/h, how far do you move while your eyes shut for 0.50 s during a hard sneeze? Problem 2: An automobile travels on a straight road for 4c km at 3d km/h. It then continues in the same direction for another 4e km at 6d km/h. (a) What is the average velocity of the car during the full 8d km trip? (Assume that it moves in the positive x direction.) (b) What is the average speed? (c) Graph x versus t and indicate how the average velocity is found on the graph. Problem 3: The position of an object moving along an x axis is given by x=3t-4t^2+t^3, where x is in meters and t in seconds. Find the position of the object at the following values of t: (a) 1.a s, (b) 2.b s, (c) 3.c s, and (d) 4.d s. (e) What is the object's displacement between t=0 and t=4.e s? (f) What is its average velocity for the time interval from t=2.e s to t=4.d s? Problem 4: The position of a particle moving along the x axis is given in centimeters by x= 9.de + 1.5c t^3, where t is in seconds. Calculate (a) the average velocity during the time interval t = 2.cd s to t = 3.dc s; (b) the instantaneous velocity at t = 2.cd s; (c) the instantaneous velocity at t = 3.dc s; (d) the instantaneous velocity at t = 2.5d s; and (e) the instantaneous velocity when the particle is midway between its positions at t = 2.cd s and t = 3.dc s. Problem 5: The position of a particle moving along an x axis is given by x = 12t^2 + 2t^3, where x is in meters and t is in seconds. Determine (a) the position, (b) the velocity, and (c) the acceleration of the particle at t= 3.dc s. (d) What is the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (i) Determine the average velocity of the particle between t = 0 and t = 3.cd s. Problem 6: In Figure below, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x-axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 2de m. If the red car has a constant velocity of 2e km/h, the cars pass each other at x = 4c.d m, and if it has a constant velocity of 40 km/h, they pass each other at x = 7d.d m. What are (a) the initial velocity and (b) the constant acceleration of the green car?
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50 s, we first need to convert the speed from km/h to m/s by multiplying by 5/18. So, Speed = 9e x 5/18 m/s Let's assume e=5 (from the student number 2021-00345), then the speed becomes 9*5*5/18 = 12.5 m/s. Now, we can calculate the distance as follows: Distance Show moreā¦
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After doing a number of the exercises with carts and fans on ramps, it is easy to draw the conclusion that everything that moves is moving at cither a constant velocity or a constant acceleration. Let's cxamine the horizontal motion of a triangular frame with a pendulum at its center that has been given a push. It undergoes an unusual motion. You should determine whether or not it is moving at either a constant velocity or constant acceleration. (Note: You may want to look at the motion of the triangular frame by viewing the digital movie entitled PASCO070. This movie is included on the VideoPoint compact disk. If you are not using VideoPoint, your instructor may make the movie available to you some other way.) The images in Fig. $2-41$ are taken from the 7 th, 16 th, and 25 th frames of that movie. Data for the position of the center of the horizontal bar of the triangle were taken every tenth of a second during its first second of motion. The origin was placed at the zero centimeter mark of a fixed meter stick. These data are in the table below. (a) Examine the position vs. time graph of the data shown above. Does the triangle appear to have a constant velocity throughout the first second? A constant acceleration? Why or why not? (b) Discuss the nature of the motion based on the shape of the graph. At approximately what time, if any, is the triangle changing direction? At approximately what time does it have the greatest negative velocity? The greatest positive velocity? Explain the reasons for your answers. (c) Use the data table and the definition of average velocity to calculate the average velocity of the triangle at each of the times between $0.100 \mathrm{~s}$ and $0.900 \mathrm{~s}$. In this case you should use the position just before the indicated time and the position just after the indicated time in your calculation. For example, to calculate the average velocity at $t_{2}=0.100$ seconds, use $x_{3}=44.5 \mathrm{~cm}$ and $x_{1}=52.1$ $\mathrm{cm}$ along with the differences of the times at $t_{3}$ and $t_{1} .$ Hint: Use only times and positions in the gray boxes to get a velocity in a gray box and use only times and positions in the white boxes to get a velocity in a white box. (d) Since people usually refer to velocity as distance divided by time. maybe we can calculate the average velocities as simply $x_{1} / t_{1}, x_{2} / l_{2}$, $x_{y} / l_{3}$, and so on. This would be easier. Is this an equivalent method for finding the velocities at the different times? Try using this method of calculation if you are not sure. Give reasons for your answer. (e) Often, when an oddly shaped but smooth graph is obtained from data it is possible to fit a polynomial to it. For example, a fourth-order polynomial that fits the data is $$\left.x=\mid\left(-376 \mathrm{~cm} / \mathrm{s}^{4}\right) t^{4}+\left(719 \mathrm{~cm} / \mathrm{s}^{3}\right) t^{3}-\left(347 \mathrm{~cm} / \mathrm{s}^{2}\right) t^{2}+(5.63 \mathrm{~cm} / \mathrm{s}) t+52.1 \mathrm{~cm}\right\}$$ Using this polynomial approximation, find the instantaneous velocity at $t=0.700 \mathrm{~s}$. Comment on how your answer compares to the average velocity you calculated at $0.700 \mathrm{~s}$. Are the two values close? Is that what you expect?
This problem is based on the analysis of a digital movie depicting a juggler. If you are using VideoPoint, view the movie entitled DSON007. Your instructor may provide you with a different movie to analyze or ask you to use the data presented in Fig. $7-38 b$. We track the motion of the white baseball of mass $0.138 \mathrm{~kg}$ in Fig. $7-38 a$, which is being caught and thrown in a smooth motion. The figure shows alternate frames depicting the catch and throw from just before to just after the juggler's hand is in contact with the ball. The data presented in Fig. $7-38 b$ include a least-squares fit for frames $33-39$ of the digital video shown in Fig. $7-38 a$. During all of these frames the ball is in contact with the juggler's hand. (Although the time codes are correct, the digital capture system missed recording a few frames between $t=1.567 \mathrm{~s}$ and $t=1.700 \mathrm{~s}$.) The goal of this problem is to consider the catch-throw process as a slow collision between the juggler's hand and the ball. In particular we would like you to verify that the impulse-momentum theorem holds for this situation. You should assume that the data and analysis presented here are correct and that Newton's Second Law is valid (a) Examine the $y$ position of the ball as a function of time for a time period during which the ball is in the juggler's hand (frames $33-39$ in Fig. $7-38 a$ ). Express each fit coefficient and its uncertainty (that is, the standard deviation of the mean) to the correct number of significant figures. Write down the equation that allows you to calculate $y$ as a function of $t$. (b) What is the nature of the vertical motion of the ball during the time it is being caught and thrown? Is its vertical velocity component zero, a constant, constantly changing, or is something else going on? Cite the reasons for your answer. What are the magnitude and direction of the vertical acceleration, $a_{y}$ of the ball? (c) Calculate the instantaneous vertical velocity of the ball just as it's being caught (frame 33). Calculate the instantaneous vertical velocity of the ball just as it's being released (frame 39). (Hints: Use three significant figures in your coefficients. You can either interpret the physical meaning of the fit coefficient $a_{1}$ and then use the kinematic equation relating velocity to acceleration, initial velocity (at $t$ $=0.000 \mathrm{~s}$ ), and time, or you can take the derivative with respect to time of the $y$ vs. $t$ equation you just wrote down in part (a).) (d) Assuming the vertical acceleration of the ball is constant while it is in the juggler's hand, what is the net vertical force on the ball during the entire catch-throw process? Draw a free-body diagram showing the magnitudes and directions of the forces on the ball. What are the magnitude and direction of the gravitational force on the ball? What are the magnitude and direction of the vertical force the juggler exerts on the ball? (e) Identify any Newton's Third Law pairs for this situation. Identify what object is exerting the gravitational force on the ball. According to Newton's Third Law, how is the ball interacting with that object? (f) Find the vertical momentum of the ball when it first falls into the juggler's hand (as in frame 33). Also find the vertical momentum of the ball when it is just about to leave the juggler's hand (as in frame 39). What are the magnitude and direction of the momentum change, $\Delta p_{y}$, in the vertical direction that the ball undergoes during this time period? Beware: Momentum is a vector quantity. Do not fall into the trap of simply subtracting the magnitudes of the two momenta. (g) How much time, $\Delta t$, does the ball spend in the hand of the juggler? Calculate the impulse transmitted to the ball by the net force on it during the catch-throw "collision." (h) Compare the change in momentum to the impulse imparted to the ball. Does the impulse-momentum theorem seem to hold to the appropriate number of significant figures?
The weight of an object is the quantity of matter it contains. a) The force with which it is attracted to the earth. b) Refers to its inertia. c) Basically the same as its mass but with different units. To keep a vehicle moving at the speed v requires a force F. The power needed is: a) F/v b) Fv c) 1/2 Fv^2 d) F/v^2 A baseball catcher throws a ball vertically upward and catches it in the same spot when it returns. At what point in the ball's path does it experience zero velocity and non-zero acceleration at the same time? a) Midway on the way up b) At the top of its trajectory c) The instant it leaves the catcher's hand d) The instant before it arrives in the catcher's hand A continuous change of position with respect to a reference point during a given time is called: a) Acceleration b) Force c) Motion d) Inertia All of the following are manifestations of the third law of motion except: a) Rowing a boat b) Launching of a rocket c) Falling objects d) Swimming A brick is dropped from rest from a height of 4.9 m. How long does it take the brick to reach the ground? a) 0.6 s b) 0.8 s c) 1.0 s d) 1.4 s A cereal box has the dimensions of 0.19 m x 0.28 m x 0.070 m. If there are 3.28 feet per meter, then what is the volume of the box in cubic feet? a) 0.13 cubic feet b) 0.04 cubic feet c) 0.012 cubic feet d) 0.003 cubic feet Ryan throws a tennis ball vertically upward. The ball returns to the point of release after 3.5 sec. What is the speed of the ball as it is released? a) 10 m/s b) 17 m/s c) 21 m/s d) 12 m/s Car A has a mass of 1000 kg and a speed of 60 km/h, and car B has a mass of 2000 kg and a speed of 30 km/h. The kinetic energy of car A is: a) Half that of car B b) Equal to that of car B c) Four times that of car B d) Twice that of car B How much work can an electric pencil sharpener do if it uses 5 watts for 5 minutes? a) 7500 Joules b) 1500 Joules c) 750 Joules d) 125 Joules A police car in pursuit with a car robber travels 200 m, 30 deg. north of east. What is the east component of this displacement? a) 2 points b) 245.7 m c) 100 m d) 123.2 m e) 173.2 m Which one of the following is not a unit of energy? a) Foot-pound b) Kilowatt-hour c) Newton-meter d) Watt The resistive force that arises to oppose the motion of an object past another with which it is in contact is called: a) Inertia b) Impulse c) Tension d) Friction If we know an object is moving at constant velocity, we may assume: a) The net force acting on the object is zero b) There are no forces acting on the object c) The object is accelerating d) The object is losing mass A student riding a bicycle moves at a speed of 5 m/s for 5 seconds, then moves at 10 m/s for another 5 seconds. What is her average speed? a) 9.5 m/s b) 7.5 m/s c) 3.8 m/s d) 3.5 m/s A ball is launched from ground level at 30 m/s at an angle of 35ĆĀ° above the horizontal. How far does it rise before it is at ground level again? a) 4.4 m b) 8.8 m c) 13.4 m d) 15.1 m A 975-kg car accelerates from rest to 26.7 m/s in a distance of 120 m. What is the magnitude of the net force acting on the car? a) 740 N b) 2900 N c) 91 N d) 1300 N A net force of 1 N acts on a 2 kg object initially at rest for 2 s. The distance the object moves during that time is: a) 0.5 m b) 2 m c) 1 m d) 4 m An 800-kg white horse has a power output of 1 hp. The maximum force it can exert at a speed of 3 m/s is: a) 2.6 kN b) 0.25 kN c) 2.2 kN d) 3.6 kN A horizontal force of 100 N is applied to move a 45-kg cart across a 9-m level surface. What work is done by the 100 N force? a) 405 J b) 500 J c) 900 J d) 4,500 J A car starting from rest accelerates in a straight-line path at a constant rate of 2.0 m/s^2. How far will the car travel in 12 seconds? a) 180 m b) 144 m c) 6 m d) 24 m If the coefficient of kinetic friction between the block and the surface is 0.30 and the magnitude of the frictional force is 80.0 N, what is the weight of the block? a) 1.6 N b) 4.0 N c) 160 N d) 267 N When the outdoor emergency warning siren at a certain school was tested, the sound from the siren took 7.0 s to reach a house located 2.40 km from the school. What is the speed of sound in air? a) 245 m/s b) 343 m/s c) 440 m/s d) 542 m/s A boy pulls a 5.0-kg sled with a rope that makes a 60.0ĆĀ° angle with respect to the horizontal surface of a frozen pond. The boy pulls on the rope with a force of 10.0 N, and the sled moves with constant velocity. What is the coefficient of friction between the sled and the ice? a) 0.09 b) 0.12 c) 0.18 d) 0.06
Umar Sohail Q.
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