A block is suspended from a spring, pulled down, and released. The blocks position-versus-time graph is shown in FIGURE P2.38. a. At what times is the velocity zero? At what times is the velocity...
A particles velocity is described by the function v x = (t 2 - 7t + 10) m/s, where t is in s. a. At what times does the particle reach its turning points? b. What is the particles acceleration at...
A particles velocity is described by the function v x = k t 2 m/s, where k is a constant and t is in s. The particles position at t 0 = 0 s is x 0 = - 9.0 m. At t 1 = 3.0 s, the particle is at x 1 =...
A particles acceleration is described by the function a x = (10 t) m/s 2 , where t is in s. Its initial conditions are x 0 = 0 m and v 0x = 0 m/s at t = 0 s. a. At what time is the velocity again...
A particles velocity is given by the function v x = (2.0 m/s) sin (pt), where t is in s. a. What is the first time after t = 0 s when the particle reaches a turning point? b. What is the particles...
FIGURE P2.45 shows a set of kinematic graphs for a ball rolling on a track. All segments of the track are straight lines, but some may be tilted. Draw a picture of the track and also indicate the...
Draw position, velocity, and acceleration graphs for the ball shown in FIGURE P2.44. See Problem 43 for more information. Figure P2.44 Vor
A ball rolls along the smooth track shown in FIGURE P2.43. Each segment of the track is straight, and the ball passes smoothly from one segment to the next without changing speed or leaving the...
The takeoff speed for an Airbus A320 jetliner is 80 m/s. Velocity data measured during takeoff are as shown. t (s) ___________ v x (m/s) 0 .. 0 10 .. 23 20 .. 46 30 .. 69 a. Is the jetliners...
Two cars are driving at the same constant speed on a straight road, with car 1 in front of car 2. Car 1 suddenly starts to brake with constant acceleration and stops in 10 m. At the instant car 1...
You are playing miniature golf at the golf course shown in FIGURE P2.51. Due to the fake plastic grass, the ball decelerates at 1.0 m/s 2 when rolling horizontally and at 6.0 m/s 2 on the slope. What...
You are at a train station, standing next to the train at the front of the first car. The train starts moving with constant acceleration, and 5.0 s later the back of the first car passes you. How...
A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s 2 for 30 s, then runs out of fuel. Ignore any air resistance effects. a. What is the...
A lead ball is dropped into a lake from a diving board 5.0 m above the water. After entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the...
A hotel elevator ascends 200 m with a maximum speed of 5.0 m/s. Its acceleration and deceleration both have a magnitude of 1.0 m/s 2 . a. How far does the elevator move while accelerating to full...
A cheetah spots a Thomsons gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this...
A basketball player can jump to a height of 55 cm. How far above the floor can he jump in an elevator that is descending at a constant 1.0 m/s?
You are 9.0 m from the door of your bus, behind the bus, when it pulls away with an acceleration of 1.0 m/s 2 . You instantly start running toward the still-open door at 4.5 m/s. a. How long does it...
Ann and Carol are driving their cars along the same straight road. Carol is located at x = 2.4 mi at t = 0 h and drives at a steady 36 mph. Ann, who is traveling in the same direction, is located at...
Amir starts riding his bike up a 200-m-long slope at a speed of 18 km/h, decelerating at 0.20 m/s 2 as he goes up. At the same instant, Becky starts down from the top at a speed of 6.0 km/h,...
A very slippery block of ice slides down a smooth ramp tilted at angle . The ice is released from rest at vertical height h above the bottom of the ramp. Find an expression for the speed of the ice...
Bob is driving the getaway car after the big bank robbery. Hes going 50 m/s when his headlights suddenly reveal a nail strip that the cops have placed across the road 150 m in front of him. If Bob...
One game at the amusement park has you push a puck up a long, friction less ramp. You win a stuffed animal if the puck, at its highest point, comes to within 10 cm of the end of the ramp without...
A motorist is driving at 20 m/s when she sees that a traffic light 200 m ahead has just turned red. She knows that this light stays red for 15 s, and she wants to reach the light just as it turns...
Your goal in laboratory is to launch a ball of mass m straight up so that it reaches exactly height h above the top of the launching tube. You and your lab partners will earn fewer points if the ball...
The two masses in FIGURE P2.75 slide on friction less wires. They are connected by a pivoting rigid rod of length L. Prove that v 2x = - v 1y tan θ. Figure P2.75 L.
A sprinter can accelerate with constant acceleration for 4.0 s before reaching top speed. He can run the 100 meter dash in 10.0 s. What is his speed as he crosses the finish line?
A rubber ball is shot straight up from the ground with speed v 0 . Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. a. At what height above the...
As an astronaut visiting Planet X, youre assigned to measure the free-fall acceleration. Getting out your meter stick and stop watch, you time the fall of a heavy ball from several heights. Your data...
When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation Where P = 3.6 Ã 10 4 watts...
You are given the kinematic equation or equations that are used to solve a problem. For each of these, you are to: a. Write a realistic problem for which this is the correct equation(s). Be sure that...
Careful measurements have been made of Olympic sprinters in the 100 meter dash. A quite realistic model is that the sprinters velocity is given by v x = a(1 - e -bt ) Where t is in s, v x is in m/s,...
Can the magnitude of the displacement vector be more than the distance traveled? Less than the distance traveled? Explain.
Can a vector have a component equal to zero and still have nonzero magnitude? Explain.
Can a vector have zero magnitude if one of its components is nonzero? Explain.
Suppose two vectors have unequal magnitudes. Can their sum be zero? Explain.
The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 50 km/s. To the crews great surprise, a Klingon ship is 100 km directly ahead, traveling in the same...
You go to an amusement park with your friend Betty, who wants to ride the 30-m-diameter Ferris wheel. She starts the ride at the lowest point of a wheel that, as you face it, rotates...
You are fixing the roof of your house when a hammer breaks loose and slides down. The roof makes an angle of 35 with the horizontal, and the hammer is moving at 4.5 m/s when it reaches the edge. What...
Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jills velocity vector was 2.5 m/s. a. What was the angle of the hill? b. What was the vertical component of Jills velocity?
Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40 from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is measured in...
Dee is on a swing in the playground. The chains are 2.5 m long, and the tension in each chain is 450 N when Dee is 55 cm above the lowest point of her swing. Tension is a vector directed along the...
Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25, and Paul is pulling a large crate up the ramp with a rope that angles 10 above the ramp. If Paul pulls with...
Tom is climbing a 3.0-m-long ladder that leans against a vertical wall, contacting the wall 2.5 m above the ground. His weight of 680 N is a vector pointing vertically downward. (Weight is measured...
A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0 m/s. A wise elder duck finally realizes that the solution is to...
A cart that is rolling at constant velocity on a level table fires a ball straight up. a. When the ball comes back down, will it land in front of the launching tube, behind the launching tube, or...
Anita is running to the right at 5 m/s in FIGURE Q4.8. Balls 1 and 2 are thrown toward her by friends standing on the ground. According to Anita, both balls are approaching her at 10 m/s. Which ball...
Zack is driving past his house in FIGURE Q4.10. He wants to toss his physics book out the window and have it land in his driveway. If he lets go of the book exactly as he passes the end of the...
In FIGURE Q4.11, Yvette and Zack are driving down the freeway side by side with their windows down. Zack wants to toss his physics book out the window and have it land in Yvettes front seat. Ignoring...
In uniform circular motion, which of the following quantities are constant: speed, instantaneous velocity, the tangential component of velocity, the radial component of acceleration, the tangential...
FIGURE Q4.13 shows three points on a steadily rotating wheel. a. Rank in order, from largest to smallest, the angular velocities Ï 1 , Ï 2 , and Ï 3 of these points. Explain. b. Rank...
In the Olympic shot-put event, an athlete throws the shot with an initial speed of 12.0 m/s at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground. How...
A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 150 m/s. How far short of the target should it...
You have a remote-controlled car that has been programmed to have velocity where t is in s. At t = 0 s, the car is at What are the cars (a) Position vector and (b) Acceleration vector at t = 2.0 s?...
Mary needs to row her boat across a 100-m-wide river that is flowing to the east at a speed of 1.0 m/s. Mary can row with a speed of 2.0 m/s. a. If Mary points her boat due north, how far from her...
FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s? Figure Ex 4.23 w (rad/s) 20- 10- t (s) 0-...
FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particles angular velocity at (a) t = 1 s, (b) t = 4 s, and (c) t = 7 s? Figure Ex 4.24 0...
FIGURE EX4.25 shows the angular-velocity-versus-time graph for a particle moving in a circle, starting from θ 0 = 0 rad at t = 0 s. Draw the angular-position-versus-time graph. Include...
The earths radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. The flight from Kampala to Singapore...
An old-fashioned single-play vinyl record rotates on a turntable at 45 rpm. What are (a) The angular velocity in rad/s and (b) The period of the motion?
As the earth rotates, what is the speed of (a) A physics student in Miami, Florida, at latitude 26, and (b) A physics student in Fairbanks, Alaska, at latitude 65? Ignore the revolution of the earth...
How fast must a plane fly along the earths equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in...
Peregrine falcons are known for their maneuvering ability. In a tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the...
To withstand g-forces of up to 10 gs, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a human centrifuge. 10 gs is an acceleration of 98 m/s 2 . If the length of the...
The radius of the earths very nearly circular orbit around the sun is 1.5 10 11 m. Find the magnitude of the earths (a) Velocity, (b) Angular velocity, and (c) Centripetal acceleration as it travels...
A speck of dust on a spinning DVD has a centripetal acceleration of 20 m/s 2 . a. What is the acceleration of a different speck of dust that is twice as far from the center of the disk? b. What would...
FIGURE EX4.36 shows the angular velocity graph of the crankshaft in a car. What is the crankshafts angular acceleration at (a) t = 1 s, (b) t = 3 s, and (c) t = 5 s? Figure Ex 4.37 w (rad/s) 250 -...
FIGURE EX4.37 shows the angular acceleration graph of a turntable that starts from rest. What is the turntables angular velocity at (a) t = 1 s, (b) t = 2 s, and (c) t = 3 s? Figure Ex 4.37 a (rad/s)...
FIGURE EX4.38 shows the angular- velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s? Figure Ex 4.38 w (rad/s) 20- 10- 0+ -t...
A wheel initially rotating at 60 rpm experiences the angular acceleration shown in FIGURE EX4.39. What is the wheels angular velocity, in rpm, at t = 3.0 s? Figure Ex 4.39 (rad/s?) 04 -t (s) 3
A 5.0-m-diameter merry-go-round is initially turning with a 4.0 s period. It slows down and stops in 20 s. a. Before slowing, what is the speed of a child on the rim? b. How many revolutions does the...
An electric fan goes from rest to 1800 rpm in 4.0 s. What is its angular acceleration?
a. A projectile is launched with speed v 0 and angle . Derive an expression for the projectiles maximum height h. b. A baseball is hit with a speed of 33.6 m/s. Calculate its height and the distance...
A gray kangaroo can bound across level ground with each jump carrying it 10 m from the takeoff point. Typically the kangaroo leaves the ground at a 20 angle. If this is so: a. What is its takeoff...
A ball is thrown toward a cliff of height h with a speed of 30 m/s and an angle of 60 above horizontal. It lands on the edge of the cliff 4.0 s later. a. How high is the cliff? b. What was the...
A tennis player hits a ball 2.0 m above the ground. The ball leaves his racquet with a speed of 20.0 m/s at an angle 5.0 above the horizontal. The horizontal distance to the net is 7.0 m, and the net...
You are target shooting using a toy gun that fires a small ball at a speed of 15 m/s. When the gun is fired at an angle of 30 above horizontal, the ball hits the bulls-eye of a target at the same...
A 35 g steel ball is held by a ceiling-mounted electromagnet 3.5 m above the floor. A compressed-air cannon sits on the floor, 4.0 m to one side of the point directly under the ball. When a button is...
A javelin thrower standing at rest holds the center of the javelin behind her head, then accelerates it through a distance of 70 cm as she throws. She releases the javelin 2.0 m above the ground...
FIGURE EX1.11 shows two dots of a motion diagram and vector 1 Copy this figure, then add dot 4 and the next velocity vector 2 if the acceleration vector at dot 3 (a) Points right and (b) Points left?...
Breathing Oxygen. The density of air under standard laboratory conditions 1.29 kg/m 3 is and about 20% of that air consists of oxygen. Typically, people breathe about L of air per breath. (a) How...
Compute the x- and y-components of the vectors A, B, C, and D in Fig. E1.28. Figure E1.28: B (15.0 m) 30.0 (10.0 m) 53.0 25.0 (12.0 m) V (8.00 m)
Determine the Jacobian matrix |J| and its determinant for the elements shown in Figure P10 11. Show that the determinant of |J|for rectangular and parallelogram shaped elements is equal to A/4, where...
Solve Problems A.1 through A.6 using matrices [A], [B], [C], [D], and [E] given by (a) |A| + |B| (b) |A| + |B| (c) |A| |C| T (d) |D| {B} (e) |D| |C| (f) |C| |D| 3 1 01 -1 0 3 2 0 [4] [B] [C] -2 8 3 1...
(a) The recommended daily allowance (RDA) of the trace metal magnesium is 410 mg/day for males. Express this quantity in g/day. (b) For adults, the RDA of the amino acid lysine is 12 mg per kg of...
Vector A has y-component A y = +13.0 m. A makes an angle of 32.0 o counterclockwise from the y-axis. (a) What is the x-component of A? (b) What is the magnitude of A?
A rectangular piece of aluminum is 7.60 0.01 cm long and 1.90 0.01 cm wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional uncertainty in the...
Two workers pull horizontally on a heavy box, but one pulls twice as hard as the other. The larger pull is directed at 25.0 west of north, and the resultant of these two pulls is 460.0 N directly...
(a) Find the magnitude and direction of the vector R that is the sum of the three vectors A, B, and C in Fig. E1.28. In a diagram, show how is formed from these three vectors. (b) Find the magnitude...
A rocket fires two engines simultaneously. One produces a thrust of 480 N directly forward, while the other gives a 513-N thrust at 32.4 o above the forward direction. Find the magnitude and...
Dislocated Shoulder. A patient with a dislocated shoulder is put into a traction apparatus as shown in Fig. P1.73. The pulls and have equal magnitudes and must combine to produce an outward traction...
A dog in an open field runs 12.0 m east and then 28.0 m in a direction 50.0 o west of north. In what direction and how far must the dog then run to end up 10.0 m south of her original starting point?
Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 26.0 m in a direction 60.0 o west of north. Jane...
John, Paul, and George are standing in a strawberry field. Paul is 14.0 m due west of John. George is 36.0 m from Paul, in a direction 37.0 o south of east from Pauls location. How far is George from...
Vectors A and B have scalar product -6.00 and their vector product has magnitude +9.00. What is the angle between these two vectors?
When two vectors A and B are drawn from a common point, the angle between them is ɸ. (a) Using vector techniques, show that the magnitude of their vector sum is given by (b) If A and B...
The scalar product of vectors A and B is +48.0 m 2 . Vector A has magnitude 9.00 m and direction 28.0 o west of south. If vector B has direction 39.0 o south of east, what is the magnitude of B?
Three sleds are being pulled horizontally on friction less horizontal ice using horizontal ropes (Fig. E5.14). The pull is of magnitude 125 N. Find (a) The acceleration of the system and (b) The...
All the stars of the Big Dipper (part of the constellation Ursa Major) may appear to be the same distance from the earth, but in fact they are very far from each other. Figure P1.101 shows the...
Sam heaves a 16-lb shot straight upward, giving it a constant upward acceleration from rest of 35.0 m/s 2 for 64.0 cm. He releases it 2.20 m above the ground. You may ignore air resistance. (a) What...