1. What is Hooke’s law? How to calculate the restoring force? 2. Why is there a negative sign in front of the restoring force?3. Mechanical springs are energy-storing devices. How to calculate the stored elastic energy?4. What is the difference between a spring scale and a balance scale
Energy and Projectile Motion Purpose: The purpose of this experiment is to investigate conservation of mechanical energy, and the relationship
Energy and Projectile Motion Purpose: The purpose of this experiment is to investigate conservation of mechanical energy, and the relationship between mechanical energy and the range of the projectile motion traveled by a small rolling object. Equipment Needed: 1.Table 2.Two coins (five-cents and quarter) 3.Ruler or tape measure with cm scale 4.Inclined flat surface (folder or thin book) 5.Thick book 6.Stick Tape 7.Scientific Calculator Theory: •When and object undergoes rolling motion on a flat surface (for example, bicycle tire), thecenter of mass of the object moves with linear velocity (v) in a straight line parallel to the surface, and the object rotates with angular velocity (ω) around the center of mass as it moves, as shown in the below diagram. •If the object rolls smoothly (no slipping) and has radius (r), then the relationship between the linear (v) and angular (ω) velocities is: v = rω•Because the motion of a rolling object is a combination of translational motion and rotational motion that occur simultaneously, then the total kinetic energy is a combination of translational kinetic energy (KET) and rotational kinetic energy (KER): KE=KET KERKE=1/2mv^2 1/2 Iw^2 Where: v = linear velocity of rolling object ω = angular velocity of rolling object m = mass of rolling object I = moment of inertia of rolling object (see below table) For smooth rolling motion (no slipping) v = rω•For this experiment, a small object (coin) rolls smoothly without slipping down an inclined flat surface (ramp) followed by projectile motion to the floor, as shown in above diagram. •The total mechanical energy of the object consists of gravitational potential energy (PE), translational kinetic energy (KET), and rotational kinetic energy (KER). •The initial gravitational potential energy of the coin relative to the tabletop is: PE = mgh Where: m = mass of coin g = 9.80 m/s^2 (free fall acceleration) h = height of the inclined surface from tabletop •The translational kinetic energy of the coin at the bottom of the incline and as it leaves the table is: KET = ½ mv^2 Where: m = mass of coin v = horizontal velocity at bottom of incline •The rotational kinetic energy of the coin at the bottom of the incline and as it leaves the table is: KER = ½ I ω^2Where: I = ½ mr^2(moment of inertia for a cylinder) ω= angular velocity at bottom of incline (v = rω) •If we assume that the coin starts from rest at the top of the incline and rolls smoothly without slipping, we can then use conservation of energy to determine the velocity (v) at the bottom of the incline: ETOT i = ETOT f⇒ PEi = KTT f KERf⇒mgh = ½ mv^2 ½ I ω^2⇒V= spr4/3gh (derive in your lab report)•As the coin leaves the tabletop, it undergoes projectile motion with ax = 0 and ay = g. •The vertical distance the coin travels from the tabletop to the floor is equal to the height of the table and can be determine from the free fall equation: y = vy t ½ at^2 Where: vyis the y-component of the initial velocity ay = g = 9.80 m/s^2 (free fall acceleration) t= time of flight” is the time. Since the coin leaves the tabletop horizontally, then the initial vertical is zero (vy = 0): y = ½ gt^2 ⇒t = sqr 2y/g•The horizontal distance (range) the coin travels from the edge of the table can be calculated from: x = vt, since in the x-direction the acceleration is zero and the velocity is constant. •Substitute the above expressions for “v” and “t” in the range equation for the horizontal distance: ⇒x= v.t= sqr 4/3gh . sqr 2y/gx=sqr 8/3 hy (derive in your lab report) •Percentage error calculation is used to compare an experimental (measured) value to a theoretical or accepted value. The equation used to calculate a percentage difference is: % Error = lTheoretical -Measuredl / Theoretica| × 100 Procedure: •Prop the incline surface up against a book, as shown in the above figure, so that one end is about 10 cm from the edge of the table and the other end is about 10 cm above the tabletop. •If necessary, tape the lower end of the incline to the tabletop to prevent it from slipping. •For part A, we will use the five-cent coin, roll it down the incline and have it undergo projectile motion to the floor. •To determine the initial x-position of the projectile motion, drop the coin from the edge of the table and mark on a sheet of paper, taped to the floor, where it falls. •Hold the coin vertically near the top edge of the incline so it can roll down the incline in a straight line, and using the ruler measure the height “h” from the bottom of the coin to the tabletop. Record “h” in the table given below. • Release from rest the coin from the top of the incline and mark on a sheet of paper, taped to the floor, where it strikes the floor. • Measure “x” the horizontal distance (range), which is the distance between the marks on the sheets of paper taped to the floor. Record “x” in the table given below. • Measure “y” the vertical distance, which is the height from the tabletop to the floor. Record “y” in the table given below. • Repeat the above procedure using the same five-cent coin for a total of 10 trials and record the measurements, to the correct number of significant figures, in the table given below. • For part B, we will use the quarter coin, roll it down the incline and have it undergo projectile motion to the floor. •Repeat the above procedure using the same quarter coin for a total of 10 trials and record the measurements, to the correct number of significant figures, in the table given below. Analysis: 1.Derive in the theory section of your lab report the above final equation for the horizontal distance/range(x). 2.Calculate the theoretical values of the range (x) for all trials. Remember to show all calculations in detail and to round the results to the correct number significant figures. Record the results in the table given below. 3.Compare to the experimental (measured) and accepted (calculated) values of the range (x) by calculating the % error. Record the results in the table given below. 4.Do you expect the experimental and accepted values of the range (x) agree? Discuss in the conclusion of your lab report. 5.Based on your results, are the experimental values of the range (x) larger or smaller than the accepted values? What do you expect and why? Explain in the conclusion and justify your answer. 6.What assumptions did we make in this experiment and are they valid? Discuss in your lab report. 7.For the two different coins (five-cents and quarter) with different mass and radius, can the same equation derived above be used to determine the range (x) and why? Do your results agree with expectations? Discuss in your lab report. 8.If we replace the coins with a marble or a block, can the same equation derived above be used to determine the range (x) and why? If it cannot be used, what would be a more appropriate equation? Explain in the conclusion of your lab report. Lab Report: •When writing the lab report, you must review and follow very carefully the Physics Lab Report instructions handout. •In your lab report, include the Cover Page, Objectives, Theory, Equipment, Data, Graphs, Calculations, Conclusions, Sources of Error, and References. •Remember to show all equations and calculations in detail and to round the results to the correct number significant digits and precision. •In the conclusions section, be sure to summarize the final results, comment on the agreement or disagreement of the results with the theory or expectations, and discuss what you personally learned from this experiment and your observations/comments. •Submit your complete lab report electronically by the due date! Physics – Online Lab: Energy and Projectile Motion Tables of Data and Results •Part A – Range using Five-Cent coin: Trial 1 2 3 4 5 6 7 8 9 10Measured “h” (cm) Measured “y” (cm) Experimental “x” (cm) Accepted “x” (cm) % Error •Part B – Range using Quarter coin: Trial 1 2 3 4 5 6 7 8 9 10Measured “h” (cm) Measured “y” (cm) Experimental “x” (cm) Accepted “x” (cm) % Error
Grade 11 Thermal energy and heat: This question states “An ice cube with a mass of 50.0g is transferred directly
Grade 11 Thermal energy and heat: This question states “An ice cube with a mass of 50.0g is transferred directly from the freezer at a temperature of -9.00 Celsius to a polystyrene cup containing 150.0 g of water at 95.0 Celsius. Calculate the final temperature of the water. Ignore any heat loss to the cup and it’s surroundings. ” 1) the part that I highlighted, why did they use the specific heat capacity of water (4200 J) instead of ice (2100J) since they are using the mass of the ice (0.050kg) 2) it is cut off but the answer is T= 50˙C
-Aisha throws a 0.60-kg ball upward. Frances, standing on a balcony above Aisha, catches the ball by exerting a
-Aisha throws a 0.60-kg ball upward. Frances, standing on a balcony above Aisha, catches the ball by exerting a 1.0-N downward force on the ball. Determine the acceleration of the ball during the time interval when Frances is catching it. (answer is not -1.67m/s^2) -A friend drops a 0.625-kg basketball from 2.6 m above you.a. Determine the force that the basketball exerts on your hands while you are catching it. Assume you decelerate the ball over a distance of 1 m. b. Determine the force that you have to exert on the ball to catch it.
-Find the flare’s maximum height if it is fired on the level salt flats of Utah.-Find the distance from its
Physics Assignment Writing Service-Find the flare’s maximum height if it is fired on the level salt flats of Utah.-Find the distance from its firing point to its landing point if it is fired on the level salt flats of Utah.-Find the flare’s maximum height if it is fired over the flat Sea of Tranquility on the Moon, where g = 1.67 m/s^2-Find the distance from its firing point to its landing point if it is fired over the flat Sea of Tranquility on the Moon, where g=1.67 m/s^2
A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on
A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.70 s for the boat to travel from its highest point to its lowest, a total distance of 0.640 m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.60 m apart.Part AHow fast are the waves traveling?Express the speed v in meters per second using three significant figures.Part BWhat is the amplitude A of each wave?Express your answer in meters using three significant figures.
Consider a long line of charge with linear charge density lumda= 4 micro C/m and a point charge q =
Consider a long line of charge with linear charge density lumda= 4 micro C/m and a point charge q = −2 micro C with mass m = 0.1 kg at coordinate 2,3 . The point charge is launched from (2,3) with v = 2000 m/s at an angle of 20° with respect to the x-axis. Find the velocity of the point charge when its x-coordinate is 5.
A participant in a study of the biomechanics of kicking a soccer ball performed a knee extension action while kinematic
A participant in a study of the biomechanics of kicking a soccer ball performed a knee extension action while kinematic data were recorded (shown as the angular movement from points a to b in the figure below). The relative knee angle prior to the beginning of the movement (i) was 72°, and the relative knee angle at the end of the movement (ii) was 149°. The time taken for the movement to proceed from positions a to b was 0.34 seconds. The distance from the participant’s knee to his ankle was 47.9 cm. What was the tangential velocity of the ankle joint during the movement (in m/s)?Express your answer in m/s to two decimal places (do not include units in your answer).
1 A fire truck and a police car both respond to an accident. The fire truck has a siren that
1 A fire truck and a police car both respond to an accident. The fire truck has a siren that makes a sound at 800 Hz if standing still. The police car’s siren sounds at 1500 Hz if standing still. (Note: the speed of sound in air is 343 m/s)a If the fire truck is already parked at the accident and the police car is approaching at a speed of 30 m/s, what is the frequency observed by the fire truck driver for the police car’s siren?b. If the police car is already parked at the accident and the fire truck is approaching at a speed of 25 m/s, what frequency is observed by the police officer for the fire truck’s siren?c. If the fire truck is driving toward the accident from the opposite direction as the police car, and the police car is moving at 35 m/s and the fire truck is moving at 25 m/s, what frequencies do they both hear for each other’s sirens? (Note this is two questions and you will have a different answer for each)d. Are these sounds higher, lower or about the same in pitch compared to standing still? Are these sounds higher, lower or about the same in volume compared to standing still? explain
Look at the roller coaster track in this image. Assume no energy is lost to friction as the roller coaster
Look at the roller coaster track in this image. Assume no energy is lost to friction as the roller coaster travels around the track.The total mass of the roller coaster is 650 kg. Use the measurements shown in the image and your knowledge of conservation of energy to answer the following questions. 1. Show all of your work as you answer these questions. a) If it takes a force of 3943 N [parallel to the track] to pull the roller coaster up to point A, and it is pulled along 105 m of track, find the work done on the roller coaster. b) Find the total energy the roller coaster has at point A if it is at rest for a brief moment before it starts to go down the hill. c) According to the Law of Conservation of Energy, what will the total energy of the roller coaster be at points B and C? d) Use the Law of Conservation of Energy to find the speed of the roller coaster at point B. e) If it takes the motor 20.0 s to pull the roller coaster to point A, find the power of the motor. f) In real life, some of the energy the roller coaster has at point A will be lost as thermal energy due to friction as it travels through the track. If the speed of the roller coaster at point C is only 19 m/s, calculate the amount of energy that was lost due to friction.
Hi there, This is apart of my AP Physics assignment due this evening at 11:00. I was able to calculate
Hi there, This is apart of my AP Physics assignment due this evening at 11:00. I was able to calculate all the values you see have a check mark ; however, all the problems that have an X or are blank are the ones I dont understand which is the 4 and 5 acceleration, experimental acceleration and % error. I asked my teacher for help, but they didnt give the help at all. Can you please help me? Thank you !
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