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 One Dimensional Motion Top

 [1] You sneeze while you are driving, and your eyes close for about 0.5 seconds during the sneeze. If you are driving at km/hr , how far does the car move during that time?

 [2] An object has a constant acceleration of m/s2 . At a certain instant its velocity is m/s . What was its velocity seconds earlier?

 [3] A car increases its speed from km/hr to km/hr in minutes . What is the acceleration of the car?

 [4] In order to take off, an airplane must reach a speed of km/hr on the runway. What is the least constant acceleration it can have in order to take off from a runway km long?

 [5] In good driving conditions (dry road, etc.), the brakes on a car with new tires can decelerate the car (slow it down) at m/s2 . If the car is traveling at m/s , how long does it take the car to stop? How far does it travel during this time?

 [6] A car starts from rest and coasts down a hill with a constant acceleration. If it goes meters in seconds , find the acceleration and the velocity after this time.

 [7] A car's velocity changes from m/s to m/s while covering meters . What is the acceleration of the car and the time it takes to do this?

 [8] A ball is dropped from a bridge and strikes the water in seconds . How fast is it moving when it strikes the water, and what is the height of the bridge (neglect air resistance)?

 [9] With what speed must a ball be thrown vertically upward to rise to a maximum height of meters ? And, how long will it be in the air?

 [10] You are speeding on the freeway going miles per hour . You see a police car with its radar gun pointed right at you, and you try to slow down quickly. Your car's brakes give you an deceleration of 17 ft/s2 (a realistic number). How long will it take you to slow down to 55 miles per hour? Is it worth even trying to slow down?

 [11] At the instant a traffic light turns green, a car starts from rest and accelerates at m/s2 . At this same instant, a truck overtakes the car traveling at the constant speed of m/s . How far from the traffic light will the car overtake the truck?

 [12] You drop a rock from rest from a bridge and note that it hits the ground below seconds later. How high is the bridge?

 [13] You throw a rock straight down at m/s from a bridge and note that it hits the ground below seconds later. How high is the bridge?

 [14] Two trains are mistakenly heading toward each other. Train #1 is going at km/hr and train #2 is going km/hr . They see each other and begin braking when they are km apart. Train brakes provide a stopping acceleration of m/s2 . Is there are collision?

 [15] You are standing on top of a building meters high, and throw a ball straight upward with a velocity of m/s . On the way down, the ball misses the building's top and falls to the ground. How long does it take to reach the ground, and how fast is the rock moving when it hits the ground?

 [16] A truck starts from rest and moves with a constant acceleration of m/s2 . Find its speed and distance traveled after seconds have elapsed.

 [17] A box slides down an incline with uniform acceleration. It starts from rest and attains a speed of m/s in seconds . What is the acceleration of the block, and the distance it moves in the first seconds ?

 [18] A train running at m/s is slowed uniformly to a stop in s . Find the acceleration and the stopping distance of the train.

 [19] A ball is thrown upward and returns to its starting point in seconds . Find its initial speed.

 [20] \symbollook{middle,25} A truck is moving at m/s . The driver suddenly sees a vacant car blocking its path meters straight ahead. After a "reaction time" \Delta t, the driver applies the brakes, which gives the truck a deceleration of m/s2 . What is the minimum \Delta t, or "reaction time" the driver can have, to stop in time, and not hit the car?

 Two Dimensional Motion Top

 [1] A marble with speed m/s rolls off the edge of a table m high. How long does it take the marble to hit the floor, and how far from the edge of the table does the marble hit the floor?

 [2] A ball is shot upward from the level ground at an angle of degrees with respect to the horizontal. It is given an initial speed of m/s . How long will it take before the ball hits the ground?

 [3] A cannon ball is shot from a cannon with a speed of m/s . The cannon is pointing above the ground at an angle of degrees . The ground is level everywhere around the cannon. How far from the cannon will the ball land?

 [4] A soccer goalie punts a soccer ball. The balls leaves the goalie's foot meter above the ground, at an angle of degrees , with a speed of m/s . The angle is measured with respect to the flat, horizontal ground. How far does the ball travel before hitting the ground?

 [5] An enemy ship is anchored in the sea m from a island defending itself. The maximum velocity a defense cannon fire a cannon ball is m/s . At what angle, with respect to sea level, should the cannon be elevated to hit the enemy ship? And, how far away from the island should the ship move to be out of range of the island's defense cannon?

 [6] A person is trapped in the snow, and a rescue plane wants to drop them some emergency supplies. The plane is flying level at an altitude of meters at a speed of m/s . How far in front of the person should the pilot drop the supplies, so that they land right on top of the trapped person?

 [7] You are playing handball, and throw a ball with a speed of m/s at an angle of degrees above the horizontal directly at a wall. The wall is m from the release point. a) How long does it take before the ball hits the wall? b) How far up the wall does the ball hit?

 [8] A ball is thrown upward at an angle of degrees and lands on the top edge of a building that is m away. The top edge of the building is m above the throwing point. How fast was the ball thrown?

 [9] A baseball it hit with an initial speed of m/s at an angle of degrees . An outfielder is meters away from the batter. What is the minimum speed the outfield would have to run, directly toward the ball, to catch it?

 [10] A baseball is hit meters above the ground, at an angle of degrees , with an initial speed of m/s . Will it clear a meter fence meters away for a home-run?

 Forces and Newton's Law Top

 [1] A force acts on a kg mass and gives it an acceleration of m/s2 . How strong is the force that does this? And, what acceleration would the force product on a kg mass?

 [2] A horizontal cable pull a kg cart along a horizontal track. The tension in the cable is N . Starting from rest a) how long will it take the cart to reach a speed of m/s ? b) how far will it have gone?

 [3] A kg car is going m/s along a level road. How large a constant retarding force is required to stop it in a distance of m ?

 [4] A kg box is sliding across the floor to the right. It slows down from m/s to m/s in s . Assuming that the force on the box is constant, find the magnitude and direction of the force.

 [5] An astronaut has a mass of kg . Compute his weight on both Earth and Mars (on Mars, g=3.8 m/s2). What is his mass on each planet?

 [6] Two blocks are connected by a rope, through a pulley as shown in this figure. The block on the table has mass m1= kg and the hanging block has mass m2= kg . The table and pulley are both frictionless. Find T, the tension in the connecting rope, and the acceleration of the blocks.

 [7] A block of mass m= kg is hanging from a rope as shown. If \theta1= degrees and \theta2= degrees . What are the tensions, T1, T2, and T3 in the two ropes?

 [8] A block of mass m= kg sits at the top of an inclined plane of angle \theta= degrees . The inclined plane has a length of d= m and is frictionless. How long does it take the block to slide to the bottom of the incline?

 [9] A block of mass m= kg is sitting on an inclined plane, whose angle is \theta= degrees as shown. Find the tension T in the rope, which is holding the block from sliding down the incline.

 [10] Two blocks are hanging over a frictionless pulley as shown. One has mass m1= kg and the other has mass m2= kg . What is the tension, T, in the rope, and what is the acceleration of the blocks?

 [11] Two blocks, one of mass m1= kg and the other of mass m2= kg are an an inclined plane as shown. The angle of the incline is \theta= degrees . Find the tension, T, in the rope that connects them through the frictionless pulley, and the acceleration, a, of the blocks.

 [12] Two blocks, one of mass m1= kg and the other of mass m2= kg both on inclined surfaces shown. The angle of the left incline is \theta 1= degrees . And other other angle is \theta 2= degrees . Find the tension, T, in the rope that connects the blocks through the frictionless pulley, and the acceleration, a, of the blocks.

 [13] This person wants to accelerate the lawn mower at m/s2 . The lawn mower has a mass of m= kg . The person pushes on the lawn mower at an angle \theta= degrees . With what force, F, should they push, in the direction shown, to do so? There are no other forces acting on the lawn mower, other than F, the person's push.

 [14] You are looking at a car coming at you, which is traveling in a circle, on a banked turn, like those found on high speed race tracks. It is a cold winter's day, and the track has a sheet of ice on it, making the surface very slippery, even frictionless. The turn is banked at an angle \theta= degrees and has a radius of m . What speed must the car travel at to 1) not slide out of the turn (up and to the left)and 2) not slide down into the turn?

 [15] A "tug-of-war" has started with an old tire in the center. Three people are pulling, as shown. Person 1, exerts F1= N has shown, straight to the left. Person 2, exerts F2= N , straight down in the figure, and person 3 exerts some force F3, at some angle \theta as shown. With what force (F3), and at what angle (\theta) should person 3 pull so that the tire doesn't move at all? \symbollook{top,20}

 [16] A block of mass m= kg originally moving at m/s coasts m on a tabletop before coming to rest. What is the coefficient of friction between the block and the table?

 [17] Two blocks are connected by a rope, through a pulley as shown in this figure. The block on the table has mass m1= kg and the hanging block has mass m2= kg . The coefficient of friction between the block and the table is \mu= The pulley is frictionless. Find T, the tension in the connecting rope, and the acceleration of the blocks.

 [18] A block of mass m= kg is pushed down an incline plane with speed v0= m/s . The angle of the incline is \theta= degrees , and it has a length of d= m and has a coefficient of friction \mu= . Will the block stop on the incline?

 [19] A thin red washer is sitting on a piece of wood. You lift the wood to an angle degrees and suddenly the coin begins to slide down. What is the coefficient of friction between the washer and the wood?

 [20] Two blocks are set up as shown here. m1 has a mass of kg . A coefficient of static friction, \mu= exists between m1 and the table it's sitting on. The diagonal rope is tied at an angle \theta= degrees . What is the maximum mass that m2 may have so that m1 does not slip off of the table?

 [21] Skid marks on a road are measured to be m long. If the coefficient of kinetic friction between the tires and road are \mu= , how fast was the car going?

 [22] Three blocks are connected with ropes and pulleys as shown here: m1 and m3 hang freely from ropes, and there is coefficient of friction \mu= between the table the m2. The mass of m2 is kg . For this problem, m1 is more massive than m3. m1= kg and m3= kg . What is the acceleration of the blocks and the tension in the ropes?

 [23] A block of mass M= kg is free to slide on a frictionless surface. Another block, of mass m= kg , is pushed against M with a force F. The contact between m and M has coefficient of friction \mu= , as shown here. What constant force is needed so that m will not slide down and fall off of M?

 [24] A block of mass m= kg on an inclined plane is pushed with a horizontal force P as shown here. The coefficient of sliding friction between the block and the surface of the inclined plane of \mu= , and the angle of the incline is \theta= degrees . What should the magnitude of P be, in order for the block to have an acceleration of m/s2 ?

 Conservation of Energy Top

 [1] A ball is dropped from meters above the ground. The ball has a mass of kg . Using conservation of energy, calculate how fast it will be traveling when it hits the ground. Note: neglect air resistance.

 [2] A ball of mass m= kg is rolled, from rest, down a metal track, starting from point A as shown. Point A is meters above the ground, and the radius of the loop in the track is R= meters . How fast is it moving at points B, C, D,E and F?

 [3] A roller coaster of mass m= kg starts from rest, at a height h= meters as shown here. It is clocked to be moving at m/s at point A. How high is point A?

 [4] A kid with a mass of m= kg slides down a slide meters high and has a speed of m/s at the bottom. How much energy was lost due to friction?

 [5] A ball is launched at an upward angle of \theta= degrees from the top of a cliff meters high, with a speed of m/s . Use conservation of energy to find how fast it will be traveling when it hits the ground.

 [6] A block is at rest at point A as shown. It slides down the track without friction until point B, where suddenly it encounters "a whole lot of friction" and eventually stops in meters . A and B are part of a circle with a radius of meters . a) how fast is the block moving at point B b) what is the coefficient of friction between the block and the track as it moves past point B?

 [7] A pendulum, made of a mass m= kg tied to the end of a string of length L= m as shown in the left figure here. This position is called the "equilibrium" or "relaxed" position of the pendulum. If pulled and released, the pendulum can can swing freely from side to side. If it is pulled up to an angle \theta= degrees as shown in the right figure, then released, what speed does it have when it again swings through the "equilibrium" position shown in the left figure?

 [8] A block of mass m= kg is moving with speed v= m/s toward a spring-plunger system. The spring has a spring constant of k= N/m . The block collides with the plunger and sticks to it. How far is the spring compressed when the block stops?

 [9] A toy gun that shoots rubber balls of mass m= kg is loaded by inserting the ball into the barrel of the gun. The spring inside the gun has a spring constant of k= N/m . When the gun is loaded, the spring is compressed by an amount x= m . The gun is pointed straight up. How far up will the rubber ball go?

 [10] Some "extreme sport fun loving person" wants to go bungee jumping. They're not sure if the cord is strong enough to stop them from hitting the ground, but decide to jump and try anyway. The bungee cord's "strength" is measured by its spring constant, which is by k= N/m . The person has a mass of m= kg . Here is a picture of how it all happens: (1) The person gets ready to jump from a platform which is a height h= meters high. (2) After falling some distance, y1= meters , the bungee cord begins to get tight. (3) The person is eventually stopped by the bungee cord, a distance y2 from the point where the cord began to get tight. The question: will the bungee cord stop the person before they hit the ground?

 [11] As shown in the left figure, a ball of mass m= kg is held at a distance h= meters above the ground. A spring with spring constant k= N/m , in a relaxed state, holds a platform a distance h0= meter above the ground. The ball is released, and falls until it sticks onto the platform. When the ball is eventually stopped by the spring, the spring is compressed down as shown in the right figure. By how much is the spring compressed?

 [12] A block of mass m= kg can slide along a curved track as shown here. The block, initially at a height h= meters above the ground is released. It slides down the frictionless track, and hits the spring-stopper to the right. The spring has a a spring constant k= N/m . How far does the spring compress when it brings the block to a stop?

 [13] A block of mass m= kg can slide along a curved track as shown here. The block, initially at a height h= meters above the ground is released. It slides down a track which is all frictionless, except for a rough zone having a length of d= meters . In this rough zone, there is friction between the block and the track with a \mu= . In either case, the block eventually hits the spring-stopper to the right. The spring has a a spring constant k= N/m . How far does the spring compress when it brings the block to a stop?

 [14] A block with mass m= kg can slide down a track with a loop in it. The loop has a radius of r= meters . From what height h must the block be slid in order to make it around the loop? Assume there is no friction in the loop.

 [15] Two blocks are connected by a rope as shown. Block m2 with mass kg hangs freely from the rope. Block m1 with mass kg is connected to the other end of the rope, and is on a rough surface with coefficient of friction \mu= . It is also also connected to a spring with spring constant k= N/m . When released, m2 will move down and m1 will move toward the right, until the spring's stretch stops the system. The question is: how far will m1 move before the system stops? (your answer will also correspond to how much the spring stretches and how far down m2 will move).

 [16] A block of mass m= kg is connected, through a pulley, to a spring with spring constant k= N/m . Initially, m is held at a level which leaves the spring unstretched. How far down will m go when released?

 Conservation of Momentum Top

 [1] A cannon, whose mass is M= kg fires a cannon ball in a horizontal direction. The cannon ball has a mass of m= kg and is fired toward the right with a velocity of v= m/s . With what speed does the cannon recoil to the left?

 [2] A man with a mass of M= kg is riding down the road on a cart that has a mass of m= kg . When he and the cart are going m/s , he suddenly jumps off in such a way that he has zero horizontal velocity. How fast is the cart moving after he jumps off?

 [3] A car of mass m1= kg is at rest at a traffic light (the car on the right). Along comes a car (the left car) with mass m2= kg and initial speed v2i= m/s and hits the car at rest. There is a big crash, and the two cars end up sticking together after the collision. What speed does the "big mess of two cars stuck together" have after the collision?

 [4] Two blocks, one of mass m1= kg and the other of mass m2= kg are attached with a rope, as shown. Between them is a spring compressed by a distance d= meters . The spring has a spring constant k= N/m . Suddenly, the rope breaks, and the spring quickly expands, pushing m1 to the left with speed v1 and m2 to the right with speed v2. What are v1 and v2?

 [5] Two cars, one with mass m1= kg and the other with mass m2= kg crash in an intersection, as shown here. Before the crash, car m1 was headed East with a speed v1i= m/s and car m2 was headed North with a speed v2i= m/s . After the crash, the cars stick together. What is the speed of the 2-car wreck after the collision, and with what angle, \theta, does it leave the crash point?

 [6] A rubber ball of mass m1= kg is moving to the right with speed v= m/s . It collides elastically with another ball of mass m2= kg , which is sitting at rest. m2 is larger than m1. What are the speeds of the balls, v1 and v2, after the collision?

 [7] A block of mass m1= kg is on a curved track, a distance h= m above the ground as shown here. When released, it slides down the track and collides elastically with another block of mass m2= kg , which is sitting at rest. m2 is larger than m1. This means that m1 will bounce back in the direction from which it came after the collision. How far back up the track will m1 bounce after the collision?

 [8] A bullet with a mass of mb= kg is speeding toward a block of mass m= kg . The bullet is moving at speed vb= m/s and the block is at rest. The bullet collides with the block, embeds itself into the block, and knocks the block over the edge. The edge is a height h= m above the ground. How far from the edge does the block m (with the bullet inside) land?

 [9] Here is a problem dealing with the most general form of an elastic collision (two things collide and bounce off of each other). There is one car, call it car #1, moving toward the right. It has an initial speed v1i= m/s , and a mass of m1= kg . There is another car, call it car #2. It can be moving, or not. Enter 0 if you want it at rest. Enter a + speed if you want it moving toward the right, or a - speed if you want it moving toward the left. The speed of car #2 is v2i= m/s and the mass of car #2 is m2= kg . The problem here is to calculate what the speed of each car will be after the collision.

 [10] A bullet moving with speed vb= m/s hits and embeds itself into a big wooden block of mass M= kg . The bullet has a mass of mb= kg . How far will the block rise after the bullet becomes embedded in it?

 Rolling and Angular Momentum Top

 [1] A solid sphere, having a mass M= kg and radius r= m is rolls with speed v= m/s toward a ramp. The moment of inertia of the sphere is I=\minifraction{2,5}Mr2 (where M and r are the mass and radius of the sphere). The ramp's angle is \theta= degrees . To what distance, h, will the ball rise up the ramp before coming to a stop?

 [2] A block of mass m= kg is hanging from a rope attached to a pulley. The pulley has a mass M= kg and a radius of R= m . The block is held fixed, then suddenly released. What is the angular acceleration of the pulley? How long after being released will the block be falling at a speed of v= m/s ? (The moment of inertia of the pulley is I=\onehalf MR2.)

 [3] A solid spherical ball, with moment of inertia I=\minifraction{2,5}MR2 rolls down the track as shown. It doesn't slip or bounce around at all, but rolls smoothly through the entire track (believe it or not!) M, the mass of the ball is kg and R, the radius of the ball is m . It starts at a height of H= m and leaves the track at a height of h= m . When it reaches the horizontal end part of the track, where the red star is, it flies off of the track. How far to the right of point A does the ball land?

 [4] A figure skater spins with her arms outstretched with an angular speed of \omega= rev/s (left figure). The moment of inertia with her arms outstretched is I1= kg m2 . She then pulls their arms in, as shown in the right figure, decreasing her moment of inertia to I2= kg m2 . What is the skater's new rate of rotation?

 [5] A boy with a mass of m= kg stands near the edge of a merry-go-round (MGR) which is not spinning. The system's (boy + MGR) total moment of inertia about the center is I= kg m2 . The boy standing at r= m from the center of the MGR suddenly jumps off in a tangential direction with a speed of v= m/s . How fast will the MGR be rotating when the boy leaves it?

 [6] A boy runs directly toward the right as shown, and jumps onto a merry-go-round (MGR) which is initially at rest. He lands at the position of the blue dot, which is a distance d= m from the center of the MGR. The boy has a mass m= kg and runs with a speed of v0= m/s . The MGR has a mass of M= kg and a radius R= m . What angular speed does the MGR + boy have after the boy lands?

 [7] Two disks are on a pole. The top one has moment of inertia I1= kg m2 and the bottom one has moment of inertia I2= kg m2 . Initially, only the bottom one is spinning at \omega0= rad/s2 . Suddenly, the top one is dropped onto the bottom one, and sticks to it without slipping. What is the final angular speed of the two-disk combination?

 [8] A block of mass m= kg is attached to a rope. The rope goes through the center of a frictionless table. The block is moving with speed v= m/s along the dotted circle shown, that has a radius of r0= m . The rope is then pulled down as shown, until the radius that the block moves around is reduced to r1= m . What is the speed of the block around this smaller circle?

 [9] A long uniform rod, of length L= m and mass M= kg can pivot freely about the red dot at its center, as shown. A bullet, with mass m= kg flies into the rod with speed v at an angle \theta= degrees as shown. If the bullet lodges into the rod and the rod is left spinning with \omega= rad/s immediately after the collision, how fast was the bullet moving?

 [10] A solid red ball with radius rb= m and mass m= kg can roll along a track with a loop in it. The loop has a radius of r= meters . From what height h must the ball be rolled in order to make it around the loop? Assume there is no friction in the loop.

 Oscillations Top

 [1] A weight of N is hung from a spring that has a spring constant of k= N/m . By how much is the spring stretched?

 [2] A car bounces up and down with a period of seconds after hitting a bump. The car has a mass of kg and is supported by 4 springs, one on each tire. Determine the value of k, the spring constant of the car's springs.

 [3] A block of mass m= kg is moving toward the left with a speed of v= m/s . It comes into contact with a spring with spring constant k= N/m and compresses it until it stops. The spring then recoils, sending the spring back toward the right. How long is the block in contact with the spring?

 [4] A big block is attached to a spring. When pulled, it oscillates back and forth with a frequency of f= Hz . A smaller block, of mass m= kg is placed on top of the big block. There is a coefficient of friction between the two blocks of \mu= . How large of an oscillation amplitude can the big block have so that the smaller block will not slip off?

 [5] When a mass m= kg is hung on a spring the spring stretches by d= m . The spring is then stretched an additional m and released, starting the mass/spring to oscillate. Determine a) the spring constant b) the angular frequency, \omega c) the frequency, f of the oscillation d) the period of the oscillation e) the amplitude of the oscillation f) the maximum velocity of the mass g) the maximum acceleration of the mass

 Gravity Top

 [1] Two people are sitting a distance r= m apart. One person has a mass m1= kg . The other person has a mass m2= kg . What is the force of gravitational attraction between the two people?

 [2] You land on a mysterious new planet, and find that it has a mass of M= kg and a radius of R= m . What acceleration due to this planet's gravity do you feel on the surface of the planet?

 [3] You are the CEO of a hot new telecommunications company and need to put a satellite in orbit above the Earth. The satellite has a mass of m= kg , and you need an orbit a distance h= m above the Earth. How fast does the satellite need to be moving to stay in orbit (e.g. what is v in the figure)?

 [4] The acceleration due to gravity at the Earth's surface is 9.8 m/s2. What is the acceleration due to gravity at a distance h= m above the surface of the Earth?

 [5] Looking through your telescope, you discover a new planet with a moon orbiting around it, much like our Moon orbits around the Earth. You figure out that this new moon orbits around its planet once every t= hours , with an orbital radius of r= meters . What is the mass of this new planet?