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Description Three identical train cars, coupled together, are rolling east at 1.5  m/s  . A fourth car traveling east at 4.2  m/s  catches up with the three and couples to make a four-car train. what is the speed of the 4 car train ?

Description A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.80 of the person's regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.

Description The coordinates of an object moving in the xy plane vary with time according to the equations x= ?5.00 sin(?t)and y =4.00?5.00 cos(?t) where ? is a constant, x and y are in meters and t is in seconds (A Determine the components of velocity of the object at t=0 (B Determine the components of acceleration of the object at t=0(C) Write expressions for the position vector the velocity vector and the acceleration vector of the object at any time t>0. (D) Describe the path of the object in an xy plot

Description A soft tennis ball is dropped onto a hard floor from a height of 1.90 m and rebounds to a height of 1.37 m. (Assume that the positive direction is upward.) (a) Calculate its velocity just before it strikes the floor.___m/s (b) Calculate its velocity just after it leaves the floor on its way back up.___m/s (c) Calculate its acceleration during contact with the floor if that contact lasts 3.50 ms.____m/s2

Description (a) A light-rail commuter train accelerates at a rate of 1.15 m/s2. How long does it take it to reach its top speed of 80.0 km/h starting from rest?  s (b) The same train ordinarily decelerates at a rate of 1.65 m/s2. How long does it take to come to a stop from its top speed?  s (c) In emergencies the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency deceleration in m/s2?  m/s2

Description Chapter 1: Summary Scientists use the Système International d’Unités, also known as the metric system of measurement. Examples of metric units are meters, kilograms, and seconds. In these systems, units that measure the same property, for example units for mass, are related to each other by powers of ten. Unit prefixes tell you how many powers of ten. For example, a kilogram is 1000 grams and a kilometer is 1000 meters, while a milligram is one one-thousandth of a gram, and a millimeter is one-thousandth of a meter. Numbers may be expressed in scientific notation. Any number can be written as a number between 1 and 10, multiplied by a power of ten. For example, 875.6 = 8.756×102. A standard is an agreed-on basis for establishing measurement units, like defining the kilogram as the mass of a certain platinum-iridium cylinder that is kept at the International Bureau of Weights and Measures, near Paris. A physical constant is an empirically measured value that does not change, such as the speed of light. In the metric system, the basic unit of length is the meter; time is measured in seconds; and mass is measured in kilograms. Sometimes a problem will require you to do unit conversion. Work in fractions so that you can cancel like units, and make sure that the units are of the same type (all are units of length, for instance). When you need to do arithmetic using scientific notation, remember to deal with the leading values and the exponents separately. For multiplication, multiply the leading values and add the exponents. For division, divide the leading values and subtract the exponents. When adding or subtracting, first make sure the exponents are the same and then perform the operation on the leading values. In all cases, if the leading value of the result is not between one and 10, adjust the result. For example, 0.12×10?2 becomes 1.2×10?3. The Pythagorean theorem states that the square of the hypotenuse of a triangle is equal to the sum of the squares of the two legs. c2 = a2 + b2 Trigonometric functions, such as sine, cosine and tangent, relate the angles of a right triangle to the lengths of its sides. Radians (rad) measure angles. The radian measure of an angle located at the center of a circle equals the arc length it cuts off on the circle, divided by the radius of the circle. Dimensional analysis is a useful tool for analyzing physical situations and checking whether calculations make sense. In dimensional analysis, dimensions are treated algebraically. We use the symbols L, T, and M to represent the dimensions of length, time, and mass. The volume of a cube, for instance, has dimensions L×L×L or L3. Equations: Prefixes giga (G) = 109 mega (M) = 106 kilo (k) = 103 centi (c) = 10–2 milli (m) = 10–3 micro (?) = 10–6 nano (n) = 10–9 Pythagorean Theorem c2 = a2 + b2 Trigonometric functions sin ? = opposite / hypotenuse cos ? = adjacent / hypotenuse tan ? = opposite / adjacent Radian measure Angle = arc length / radius = s/ r 360° = 2? rad WE DO 1.  The following variables are commonly seen in equations. The name of the quantity represented by each variable, and its dimension(s), are also shown. x distance (L); t time (T); m mass (M); a acceleration (L/T2); v speed (L/T); F force (ML/T2) Using the information above, check the boxes of the equations that are dimensionally correct. Select all that apply. F = ma; v2 = 2ax; v = at2; F/v = m/t 2. The dimensions for force are the product of mass and length divided by time squared. Newton's second law states that force equals the product of mass and acceleration. What are the dimensions of acceleration? T2   T2/L  L/T2   L/T 3.  Multiply 3.65×1023 by 4.12×10154 by 1.11×10?11 and express the answer in scientific notation 4.  A drug company has just manufactured 50.0 kg of acetylsalicylic acid for use in aspirin tablets. If a single tablet contains 500 mg of the drug, how many tablets can the company make out of this batch? 5.  Newton's second law states that the net force equals the product of mass and acceleration. A boat's mass of is 9.6×105 kg and it experiences a net force of 1.5×104 kg·m/s2. State its acceleration. YOU DO (#1, due 8.31.15) 1.  Sara has lived 18.0 years. How many seconds has she lived? Express the answer in scientific notation. Use 365.24 days per year for your calculations. 2.  The world's tallest man was Robert Pershing Wadlow, who was 8 feet, 11.1 inches   tall. There are 2.54 centimeters in an inch and 12 inches in a foot. How tall was   Robert in meters?

Description Midterm If a freely falling rock were equipped with a speedometer, by how much would its speed readings increase with each second IF it were on a planet where g = 20 m/s2? Show all work leading to your answer. An airplane has a gun that fires bullets straight ahead at the speed of 600 miles per hour when tested on the ground while the plane is stationary. The plane takes off and flies east at 600 miles per hour. Explain whether each of the following is possible for the pilot to measure: When fired directly ahead the bullets move eastward at a speed of 1200 miles per hour When fired in the opposite direction (by turning the gun westward, but not the plane), the bullets drop vertically downward If fired vertically downward (by turning the gun downward, but not the plane), the bullets move eastward at 600 miles per hour while they fall. A falling 50-kg skydiver experiences an upward acceleration of 6.2 m/s2 when she opens her parachute. Show (by calculation) how much drag force is produced by the parachute. Leon’s bicycle wheels have a circumference of 2 m. What is his linear speed when the wheels rotate at 1 revolution per second? Show all work leading to your answer. At a particular point, a satellite in an elliptical orbit has a gravitational potential energy of 7000 MJ with respect to Earth’s surface and a kinetic energy of 4000 MJ. At another point in its orbit, the satellite’s potential energy is 2000 MJ. What is its kinetic energy at that point? Show all calculations leading to your answer. If a stationary cart is struck head-on by a cart with twice mass of the stationary one and a velocity of 5 m/s, what will be the new velocity of the stationary cart if the collision is inelastic? Show all calculations leading to an answer. A 2.0-gram bullet is shot into a tree stump. It enters at a speed of 3.00 x 104cm/s and comes to rest after having penetrated 0.05 m in to the stump. What was the average force during the impact? Show all calculations leading to an answer. Final Consider eight,eight-cubic centimeter (8 cm3) sugar cubes stacked so that they form a single 2 x 2 x 2 cube. How does the surface area of the single, large cube compare to the total surface area of the individual eight cubes? Report your answer as a ratio. Be sure to show all calculations leading to an answer. A rectangular barge 7 m long and 2 m wide floats in fresh water. How much will the barge sink when loaded with 600 kg of sand? Show all calculations leading to an answer. In a lab experiment, 45 grams of a metal are heated from 22?C to 78?C by the addition of 450 J of heat. What is the specific heat of the metal? Show all calculations leading to an answer. A photon of light has a wavelength of about 600 nm (1nm = 1 x 10-9 m). What is the energy of this photon of light? Show all calculations leading to an answer. An ammeter indicates the current for a toaster is 5.0 amps when the toaster is connected to 120-V circuit. How much energy is given off by the toaster in 55.0 seconds? Show all calculations leading to an answer. The isotope, Carbon-14 emits beta radiation and has a half live of 5730 years. How long will it take for the amount of radiation this gives off to drop by a factor of 4? The total U.S. consumption of electricity in a particular year was 5.0 x 1012 kilowatt-hours. What is the mass equivalence of this amount of energy? Show all calculations leading to an answer. When uranium-238 emits an alpha particle, what isotope is created? Show the nuclear equation for this reaction.

Description A 40-g block of ice is cooled to ?72°C and is then added to 620 g of water in an 80-g copper calorimeter at a temperature of 23°C. Determine the final temperature of the system consisting of the ice, water, and calorimeter. (If not all the ice melts, determine how much ice is left.) Remember that the ice must first warm to 0°C, melt, and then continue warming as water. (The specific heat of ice is 0.500 cal/g · °C = 2,090 J/kg · °C.)

Description A proton (mp = 1.673 × 10–27 kg) and an electron (me = 9.109 × 10–31 kg) are confined such that the x position of each is known to within 1.50 × 10–10 m. What is the ratio of the minimum uncertainty in the x component of the velocity of the electron to that of the proton, ?ve/?vp?

Description A subatomic particle X spontaneously decays into two particles, A and B, each of rest energy 1.40 × 102 MeV. The particles fly off in opposite directions, each with speed 0.827c relative to an inertial reference frame S. Reference: Ref 28-1 Determine the kinetic energy of particle B (relative to frame S).