All_Quizzes_4A (1)

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Nov 24, 2024

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Quiz 1.1 - Kinematics 1. A 16 story apartment building is 80 meters tall. A resident on the 8th floor steps out on to the ledge (40 meters off the ground), and throws a ball straight up, such that it just barely reaches the roofline, before turning around and falling to the ground. At the exact same moment the ball was released, another resident on the ground floor throws a rock straight up into the air. The rock and the ball hit the ground at the exact same time. What was the maximum height reached by the rock? 2. In the first part of its journey, a car uniformly accelerates from rest to a speed of 20 m/s, in a time of 4 seconds. The rest of the trip is graphed in the figure shown above. The car's deceleration in part C is twice the magnitude of its acceleration in part A. What total distance did the car travel? 3. An object moves along the x-axis according to the equation: x = 50 + 9t 2 - 0.8t 3 ( Although the units are not expressed in the equation, assume all distances are in meters, velocities in m/s, and acceleration in m/s 2 ) A) What is the initial acceleration of the object? B) What is the average velocity for the first 2 seconds of motion? C) What is the instantaneous velocity at t=2s? D) What is the maximum position reached by the object?

Quiz 1.2 - Motion in 2D 1. A carnival game requires the participant to toss a golf ball through a small elevated ring (something like a scaled-down version of shooting a basketball free throw). The narrow hoop is elevated exactly 4.00 m above the participant’s release point. In one particular winning toss, the ball descends with a total speed of 7.5 m/s at the instant is passes through the hoop, traveling at an angle of 50 o from the horizontal. ( You do not necessarily need to answer the following questions in the order they are presented. ) A) How much time elapses from the moment the ball is released until it passes through the hoop/ring? B) How far back (horizontally) is the participant from the hoop? C) What is the maximum height reached by the ball along its trajectory? D) What was the ball’s initial velocity at the moment of release (state both the speed and the angle)? E) If the ball passes cleanly through the hoop with no collision, how far away (measured horizontally) will it be when it returns to the elevation from which it was released? 2. Jesse keeps his motorboat tied to a dock on the bank of a river. The boat has a cruising speed of 4.5 m/s in calm water. Walter lives 1.6 km downstream from Jesse, with a dock on the same bank of the river. The river flows at a steady 3.5 m/s for the entire length. A) How many minutes does it take Jesse to make a round trip from his dock to Walt’s and back? Gus lives on the opposite bank of the river. His dock happens to be directly across the 63 meter wide river from Jesse’s dock. B) What is the least possible time in which Jesse’s boat can get from one bank of the river to the other? C) Assuming Jesse can jog at 2.8 m/s, what total amount of time would it take Jesse to boat across the river and jog along the shore in order to get from his own dock to Gus’s, while minimizing the amount of time spent in the boat? D) If instead, Jesse is on crutches and would prefer not to have to walk or jog along the river bank at all, at what angle should he point his boat to arrive at Gus’s dock? E) How much time elapses for the river crossing described in part (D) above? 3. An object starts from rest and begins to move around a circular path, while uniformly increasing in speed. After 5 seconds have elapsed, the object has traveled a distance of 30 meters, at which point its centripetal acceleration is exactly half as great in magnitude as its tangential acceleration. What is the radius of the circular path?

Quiz 2.1 - Newton’s Laws 1. A 125 gram toy car starts from rest and rolls down a ramp 85 cm long angled at 40 o , as shown below. The car proceeds to roll off a desk 70 cm tall, before striking the ground. Friction and air resistance are negligible. A) Draw a FBD for the car while it is on the incline. B) What is the car’s uniform acceleration while on the ramp? C) With what horizontal speed does the car project off the desk? D) What is the value of “x” (indicated in the diagram above)? E) What is the car’s angle of impact with the ground? 2. The system of blocks shown above is released from rest. What is the tension in the short segment of string (shown in blue)? 3. A physics student stands on a bathroom scale, in an elevator, on the top floor of the science building. While at rest on the top floor, the scale reads 686 N. The student then presses the button to take the elevator to the bottom floor. Just before coming to rest, the scale momentarily reads 791 N. What was the elevator's rate of change of speed, in the final moment before coming to rest?

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Quiz 2.2 - Applying Newton’s Laws 1. The two blocks on the incline (both labeled as "m") have identical mass. All of the blocks and the ramp are made of the same material, so the coefficients of friction for all surfaces are identical, and can be labeled as "μ". A) Derive an expression for the lowest possible coefficient of static friction, that can keep the system at rest, at the indicated angle "θ". Answer in terms of all of the identified variables and any other fundamental constants. B) It so happens that the coefficients of friction are actually: μ s = 0.6 and μ k = 0.5 Assuming M = 10 kg, m = 5 kg, and θ = 36.9 o , what is the acceleration of the system? 2. A rotating cylinder has a hollow section in the shape of a cone, as shown in the diagram above. A block of mass "m" contacts the sloped inner wall of the rotating system. At the indicated rotational speed "ω", the block almost begins to slide up the incline (in other words "ω" represents the fastest rotational speed for which frictional welding is not disrupted). A) Draw a FBD for the block, when it is in the position shown in the diagram. Draw a 2nd FBD with forces resolved into components. B) The height of the rotating cylinder is 66cm, and the block maintains a vertical position at h/2. What is the radius of the block's circular path, as the system rotates? C) Assuming θ = 36.9 o , m = 20 kg, and μ s = 0.6, what is the maximum value of ω, expressed in rad/s?

Quiz 3.1 - Work, Energy, & Power 1. A 200 gram object is under the influence of a net force that acts exclusively along the x-axis with a value that can be determined according to the equation: F = 0.30x 2 – 10.8 ( assuming all numerical values imply proper metric units ). The object is initially at the origin and moving in the +x direction with a speed of 22 m/s. A) What is the initial kinetic energy of the object (at the origin)? B) At what position does the object’s acceleration change fro m being a negative value, and start to become a positive value? C) How much work is done on the object as it moves from the origin to the position x = 5.0 meters? D) What is the speed of the object at x = 5.0 meters? E) What is the instantaneous power being delivered to the object when x = 5.0 meters? 2. A single flight of stairs in a particular high-rise building is 1.8 meters. A) In what amount of time would a 66 kg person have to run up five flights of stairs, in order to produce an average power output of 1 kW? B) In what amount of time would they have to run up the same stairs, in order to produce 1 hp? (1 horsepower is equal to 746 Watts.) C) In your own words, explain what a kilowatt-hour is.

Quiz 3.2 - Conservation of Energy 1. A 10 kg block is dropped from a distance y = 4.05 m above an ideal spring with a stiffness of 555 N/m 2. A curious physics student is on vacation at her lake house. She grabs hold of the rope swing in the back yard, and swings starting from rest, using a rope with a length of 9 meters.

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Quiz 3.3 - Impulse & Momentum frictionless surface 1. The two blocks shown above are initially traveling toward each other on a frictionless surface. The front of each block is lined with Velcro © , forcing the blocks to stick together as one combined mass after the collision. A) What percentage of the system’s initial kinetic energy is converted to thermal energy in this collision? The Velcro © is removed from each block, and replaced with ideal rubber bumpers, forcing the collision to be elastic. The blocks are once again set in motion with the same velocities as the previous collision. B) What is the final speed of each block after this collision? 2. The radius of the frictionless loop shown above is 40 cm. m block = 280 grams m bullet = 20 grams The bullet is shot at and becomes embedded in the block. What minimum initial speed must the bullet have (u bullet ), in order to just barely make the bullet/block combination complete the loop?

Quiz 4.1 - Rotational Kinetic Energy 1. Two blocks (one of mass “m” and the other of mass “2m”) are attached by a string that passes over a solid pulley of radius “R” and mass “m/2”, as shown in the diagram above. Friction between the ramp and the block of mass “m” is negligible. The system is released from a state of rest, and the block of mass “2m” falls through a vertical displacement of “h” before striking the ground. What is the speed of both blocks at the instant just before the block of mass “2m” hits the ground? Answer in terms of the given variables and any other fundamental constants. 2. A uniform rod, like the one shown above, is rotated about an axis through its center. Show that the moment of inertia of the rod about such an axis is 1/12 Mℓ 2 . Show each step of your derivation explicitly, in numbered steps, making all substitutions clear. You may want to add comments to some steps of your derivation for clarity. 1) Start with the equation: I=∫dI =∫r 2 dm 2) Assign variables to label the diagram shown above 3) 4) etc… continue with as many numbered steps as required, clearly justify each substitution or mathematical step in your work

Quiz 4.2 - Torque & Angular Momentum 1. A thick-walled cylinder with a mass of M, has inner radius R/2 and outer radius R, as shown above. A string is wrapped around the perimeter of the cylinder, and is held firmly, as the cylinder is released from rest. Answer all of the following questions in terms of the given variables… A) What is the rotational inertia of the cylinder about an axis passing through point “p”? B) What is the angular acceleration of the cylinder as it descends? C) What is the tension in the string? 2. A dart of mass m is traveling with a speed v o , before striking a uniform rod of mass 3m and length ℓ , at a point ¼ ℓ from the bottom of the rod (the rod hangs vertically from a hinge at the ceiling). The dart becomes permanently lodged in the rod. Answer all of the following questions in terms of the given variables… A) What is the angular speed of the system immediately after the collision occurs? B) How far from the hinge is the center of mass of the system? Measurement show that v o = 5 m/s, and ℓ = 3.9 m C) How many degrees does the rod/dart system rotate, before momentarily coming to rest and swinging back the other direction?

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Quiz 4.3 - Equilibrium & Elasticity 1. A heavy ladder of mass M and length ℓ is leaning against the side of a house. The exterior wall of the house has vinyl siding and can be treated as frictionless. A) The coefficient of static friction between the feet of the ladder and the ground is 0.25. What is the smallest angle relative to the ground that the ladder can lean without slipping? * Although you will most likely round off your answer for θ min to a few sig figs, it is recommended you make note of the answer to as many sig figs as your calculator gives in the margin of your paper... you will need the unrounded value for part (B) below: B) The ladder is leaning at the angle found in part (A), but rubber pads are added to the feet, increasing the coefficient of static friction from 0.25 to 0.30. The ladder slips when a person climbs a distance 2/3 ℓ up the ladder. What is the mass of the per son (expressed as a multiple of "M")? 2. The uniform beam in the figure above has a mass of 15 kg. The barrel hanging from the end has a mass of 20 kg. A) What is the tension in the cable? B) What is the total magnitude of the force exerted on the beam at the hinge? C) The force exerted by the hinge on the beam is directed at what angle?

Quiz 5.1 - Fluids 1. A spigot (aka a hose bib) is used to fill a bucket with fresh water. It takes 2.5 minutes to collect 30.0 liters of water. A) What is the flow rate in m 3 /s? The exit hole at the hose spigot has a radius of 8.00 mm. The spigot is fed by a water pipe with a radius of 2.00 cm, buried 18.0 cm below ground. B) What is the speed of the water as it exits the spigot? C) What is the speed of the water in the underground supply line? D) What is the gauge pressure in the supply line? 2. A vessel is filled with seawater (with a density of 1030 kg/m 3 ). A) The vessel has a depth of 80 cm. What is the absolute pressure at the bottom of the vessel? B) A solid plastic sphere with a radius of 15 cm is placed in the vessel. The sphere floats with exactly half of its volume submerged. What is the mass of the sphere? C) The sphere is removed and a hole is opened near the bottom of the vessel to allow it to drain. The seawater initially drains at a rate of 9.7 x 10 -5 m 3 /s. What is the diameter of the hole?

All_Quizzes_4A (1)

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