Topic 2: Forces and Interactions

A subway train leaves a station from rest and speeds up uniformly along a straight track. After 8.0 s its speed is 12 m/s. What is the magnitude of its acceleration?

A curling stone slides in a straight line across level ice and slows down with a constant acceleration. It passes a first line at 3.0 m/s and a second line, 20.0 m farther on, at 1.0 m/s. How much farther does it slide past the second line before it stops?

A ball is dropped from rest from a window 20.0 m above the ground. Air resistance can be ignored, and g = 9.8 m/s². How long does the ball take to reach the ground?

A student drops a rock from rest from a bridge over the Hudson River, and it hits the water 2.5 s later. Air resistance can be ignored, and g = 9.8 m/s². How fast is the rock moving just before it hits the water?

The graph shows the velocity of a cyclist on a straight bike path over 14 s. What is the cyclist's average speed for the whole 14 s?

A marble rolls off the edge of a horizontal lab bench 0.90 m above the floor with a horizontal speed of 1.5 m/s. Air resistance can be ignored, and g = 9.8 m/s². How far from the foot of the bench, measured horizontally, does the marble land?

In a demonstration, a 0.10 kg ball is dropped from rest at the same instant that a 0.50 kg ball is launched horizontally at 6 m/s from the same height above a level floor. Air resistance can be ignored. Which ball reaches the floor first?

A soccer ball leaves a player's foot at 15 m/s at an angle of 30 degrees above the horizontal. What is the vertical component of its initial velocity?

A soccer ball is kicked from level ground at 15 m/s, 30 degrees above the horizontal. Air resistance can be ignored, and g = 9.8 m/s². What is the greatest height the ball reaches?

A robot cart starts from rest at time 0 and moves in a straight line down a school hallway. The table gives its position each second. What is the cart's acceleration, assuming it is constant?

A model rocket is launched straight up from rest. Its engine gives it a constant upward acceleration of 15 m/s² for 2.0 s, and then the engine stops. Air resistance can be ignored, and g = 9.8 m/s². What is the greatest height above the launch point that the rocket reaches?

A worker pushes a 25 kg crate across a level warehouse floor with a constant horizontal force of 120 N. A motion sensor records the crate's velocity each second (table). What is the magnitude of the friction force on the crate?

A 1500 kg car moves along a straight, level road at 24 m/s when the driver sees a deer ahead. During her reaction time of 0.80 s the car keeps its speed; then the brakes apply a constant backward force of 9000 N until the car stops. What total distance does the car travel from the moment she sees the deer until it stops?

A 60. kg student stands on a bathroom scale in an elevator. The elevator is speeding up as it moves upward, with an acceleration of 1.2 m/s². Take g = 9.8 m/s². What force does the scale exert on the student?

A loaded truck and a small car collide head-on. During the collision, how do the force of the truck on the car and the force of the car on the truck compare, and which vehicle has the greater acceleration?

A 25 kg traffic signal hangs at rest from two vertical cables. The tension in one cable is 110 N. Take g = 9.8 m/s². What is the tension in the other cable?

A car drives around a flat, circular curve at a constant speed of 15 m/s. Which describes the direction of the car's acceleration?

A 0.40 kg puck on a frictionless air table is tied to a string fixed at a pin and moves in a horizontal circle of radius 0.50 m. It makes one full revolution every 2.0 s. What is the magnitude of the force the string exerts on the puck, to two significant figures?

Two boxes sit side by side, touching, on a frictionless floor. A worker pushes horizontally on the 6.0 kg box with a force of 24 N, and it pushes the 2.0 kg box ahead of it. What force does the 6.0 kg box exert on the 2.0 kg box?

Students pull a wooden block across the same lab table at a constant velocity with a spring scale held level. They add masses to the block and record the scale reading each time (table). Which claim do the data best support?

A 2.0 kg cart rolls down a ramp tilted 30 degrees above the horizontal. Friction and air resistance can be ignored, and g = 9.8 m/s². What is the magnitude of the cart's acceleration along the ramp?

A 75 kg skydiver falls at a constant terminal speed of 55 m/s before opening her parachute. Take g = 9.8 m/s². What is the air resistance on her?

On a level track with negligible friction, a 3.0 kg cart moving east at 2.0 m/s hits a 1.0 kg cart at rest. Just after the collision, the 3.0 kg cart is still moving east, at 1.0 m/s. What is the velocity of the 1.0 kg cart just after the collision, and what happens to the carts' total kinetic energy?

On a level track with negligible friction, a 2.0 kg cart moving east at 3.0 m/s hits a 1.0 kg cart at rest. The carts stick together. What is their velocity just after the collision?

On a frictionless track, a 1.5 kg cart moving east at 4.0 m/s collides head-on with a 0.50 kg cart moving west at 2.0 m/s. The carts lock together. What is their velocity just after the collision?

A 60. kg skater stands at rest on smooth ice, where friction can be ignored. She throws a 3.0 kg ball forward at 8.0 m/s. What is her velocity just after the throw?

In a crash, an airbag inflates in front of the driver. Compared with hitting the steering wheel, why does the airbag reduce the force on the driver?

A 0.060 kg tennis ball hits a wall at 20. m/s and bounces straight back at 15 m/s. It is in contact with the wall for 0.010 s. What is the magnitude of the average force the wall exerts on the ball?

A class designs a box to protect a raw egg dropped 3 m onto a sidewalk. Which design change would most reduce the force on the egg when the box lands?

Engineers test three helmet liners. In each test, a 5.0 kg headform wearing the helmet hits a rigid block at 5.0 m/s and stops without bouncing. The table gives the stopping time for each liner. Which liner gives the smallest average force on the headform, and about how large is that force?

Two carts are held together at rest on a level track with a compressed spring between them, then released so they move apart in opposite directions. Friction is negligible. A student records each cart's mass and speed after release in four trials (table). Which trial's data do not support conservation of momentum?

Two carts collide on a level track where friction and air resistance are negligible. Why is the total momentum of the two-cart system the same before and after the collision?

An astronaut has a mass of 80. kg on Earth. On the Moon, the gravitational field strength is 1.6 N/kg. What are her mass and her weight on the Moon?

A satellite orbits 2.0 Earth radii from Earth's center, where Earth's gravitational force on it is 2400 N. The satellite is moved to an orbit 4.0 Earth radii from Earth's center. What is Earth's gravitational force on it there?

A 500. kg space probe is at a height above Earth's surface equal to one Earth radius. At the surface, the gravitational field strength is 9.8 N/kg. What is the gravitational force of Earth on the probe at that height?

Two small charged spheres are 0.30 m apart, center to center. One has a charge of +3.0 × 10⁻⁶ C and the other −2.0 × 10⁻⁶ C. Use the reference tables. What is the electrostatic force between them?

Two small charged spheres exert an electrostatic force of 36 N on each other. The charge on one sphere is doubled, and the distance between their centers is tripled. The other charge does not change. What is the new force?

A small sphere with a fixed negative charge sits on an insulating stand. Point P is 5 cm to the right of the sphere. Which describes the direction of the electric field at P and the direction of the force on an electron placed at P?

Two identical small metal spheres carry equal negative charges. When their centers are 10. cm apart, each sphere pushes the other away with an electrostatic force of 0.90 N. How many excess electrons are on each sphere? (The elementary charge is 1.60 × 10⁻¹⁹ C.)

A student measures the electrostatic force between two small charged spheres at three center-to-center distances (table, an invented data set). Next, the charge on each sphere is doubled, and the spheres are placed 3.0 cm apart. If the pattern in the table holds, what is the magnitude of the force each sphere now exerts on the other?

Students wrap insulated wire around an iron nail and connect it to a power supply. They test how the number of turns of wire affects how many paper clips the nail can lift. Which variable must they keep the same in every trial?

Students record how many identical paper clips an electromagnet lifts for different numbers of turns and currents (table, an invented data set). If the pattern in the table continues, how many clips would 40 turns lift at a current of 0.75 A?

A coil is connected to a galvanometer whose needle swings right or left depending on the direction of the current. When the north pole of a bar magnet is pushed into the coil at a steady speed, the needle swings 4 divisions to the right. The magnet is turned around, its south pole is pushed into the coil and held still, and then the magnet is pulled back out at twice the earlier speed. What does the needle do while the magnet is being pulled out?

A long straight wire carries a steady current. What is the shape of the magnetic field lines around it?

Students drop the same bar magnet from rest, north pole first, through the same short coil connected to an ammeter, from three heights measured to the top of the coil. They record the peak current each time (table, an invented data set). Air resistance can be ignored. Which explanation of the pattern do the data best support?

Students move the same bar magnet into or out of coils of the same wire at steady speeds and record the peak current (table, an invented data set). A positive current means the needle swings right. If the pattern holds, what peak current would a 300-turn coil give when the N pole is pulled out at 0.40 m/s?

In a hand-crank flashlight, turning the crank spins a magnet next to a coil of wire connected to a bulb. Why does the bulb glow brighter when the crank is turned faster?

A strong magnet dropped down a vertical copper pipe falls much more slowly than the same magnet dropped down a plastic pipe of the same size. Copper is not attracted to magnets. Which explains the slower fall?