2.2-1. Draw a qualitative graph of a) the velocity b) speed c) displacement d) the distance as a function of time when a billiard ball moves towards a wall, bounces straight back without losing energy and comes to rest in a "hole" some distance from the starting point in the opposite direction to where it first moved.

2.4-1. Draw two possible graphs each of a) acceleration b) velocity as a function of time for a ball thrown upwards and falling back down to the ground.

2.6-1. A ball is thrown up with 5.0 ms^-1. After what time is it moving down with 3.0 ms^-1? [0.82 s]

2.6-2. A train is decelerated from 108 kmh^-1 to 18 kmh^-1 while moving 400 m forwards. Find the acceleration. [-1.1 ms^-2]

2.6-3. A car accelerates uniformly from 20 ms^-1 for 8.5 s while moving 230 m forwards. Find the acceleration. [1.7 ms^-2]

2.6-4. A ball rolls from the initial velocity u to rest, decelerating uniformly. Derive an expression for the initial velocity as a function of the displacement and time to come to rest. [u = 2s/t]

2.6-5. A ball is thrown from 1.8 m above the ground with the initial velocity 14 ms^-1 up and falls back to it. Find the time. [3.0 s]

2.7-1. A car with the mass 850 kg is decelerated from 40 ms^-1 by the net force 200 N for 2.3 seconds. How far will it move during this? [91 m]

2.8-1. The horizontal pulling force acting on a book on a table increases linearly with time. Draw a graph of it and the force of static friction as a function of time in the same coordinate system.

2.8-2. An object is given the initial speed 14 ms^-1 up a slope inclined 33^o where the friction coefficient is 0.12. How far will it have moved when the velocity has dropped to 5.0 ms^-1 ? [13.5 m]

2.8-3. Estimate the order of magnitude of the kinetic (dynamic) friction coefficient for car with summer tires on newly fallen snow, using relevant values you find reasonable.[hint: think of a car decelerating to rest, estimate reasonable values for relevant quantities]

2.9-1. A 70 kg box is pulled 15 m along a horisontal floor by an 80 N force doing the work 350 J in this. At what angle up from the horisontal level is the force acting? [73^o]

2.9-2. A bomb is dropped from a hovering helicopter at the altitude 4400 m. If we ignore the energy lost to air resistance, what will the ground impact speed be? [294 ms^-1]

2.9-3. A pump moves 50 liters of water per minute 3.70 meters up. Find its power if the efficiency is 71 %. [43 W]

2.10-1. When a "massless" spring is compressed 7.5 cm it acts with a force of 3.4 N on a 500 g object attached to it. If the same spring with the same object is stretched out 13 cm from its equilibrium and then released, what speed will the object have when it has been pulled back to 4.0 cm from the equilibrium, still on the same side of the equilibrium as when it was released? [1.2 ms^-1]

2.11-1. Show that the kinetic energy depends on momentum and mass as E_k = p²/2m.

m11-2. A rolling ball A moving at 5.0 ms^-1 hits another ball B with twice its mass being at rest. B is given the velocity 2.3 ms^-1 in a direction 25 degrees to the right from the one A was moving in before the collision. What is the magnitude and direction (angle to original direction) of A's velocity after the collision? [67^o to the left of A's original direction, speed 2.1 ms^-1]

2.11-3. A 900 kg car coming from the north at 20 ms^-1 collides head-on with one coming from the south at 28 ms^-1 with the mass 750 kg. If the cars stay together after collision, find the velocity of the wreck. [1.8 ms^-1 to the north]

2.11-4. A 120 g ball moving at +2.1 ms^-1 hits a 190 g ball at rest in an elastic collision. Find the velocities of the balls after the collision, assuming that they are parallel to the first ball's initial velocity. [- 0.47 ms^-1 and +1.63 ms^-1]

2.11-5. The net force acting on a 5.0 kg ball is described by a graph of force as a function of time with lines through the points (0s, 0N), (3s, 140N), (8s, 0N). The velocity of the ball at t = 0s is 15 ms^-1 in a direction opposite to that of the force at t = 3s. Find the velocity of the ball at t = 8 s. [97 ms^-1]

2.11-6. Estimate the order of magnitude of the a) momentum b) kinetic energy of a running cat.

2.12-1. An object is shot at the initial velocity 44 ms^-1 in a direction 35^o upwards from a cliff 80 m above sea level. Find a) the maximum altitude of the object [112 m above sea] b) the time it takes to reach it [2.57 s] c) the range (how far it travels horizontally) [265 m] d) the speed it hits the water with [59.2 ms^-1]e) the angle it hits the water with [52.5^o down from the horizon]

2.13-1. A wrench exerts the torque 100 Nm on a nut when it is pulled with the force 1600 N acting at a distance of 32 cm from the pivot point in the nut. Which two possible angles between the force and the wrench arm can you find? [11.3^o and 168.7^o]

2.13-2. A 7.0 m long seesaw is in balance when a 50 kg person is sitting at one end and a 70 kg is sitting - where? [2.5 m from pivot]

2.13-3. A 4.00 m long 33 kg uniform beam is held horisontally in place by vertical ropes attached to each end. A 15 kg object is hanging from a point 1.20 m from one end. Find the (forces of) tension in the ropes.[206 N and 265 N]

2.13-4. A 500 kg load is hanging from the end of a 5.50 m long 64 kg uniform beam attached to a wall at a 40^o angle to the vertical direction. A horisontal rope is attached to the midpoint of the beam and the wall. Find a) the tension in the rope [8758 N] b) the direction and magnitude of the reaction force of the wall on the beam. [58^o from vertical direction, magnitude 10359 N]]

2.14-1. The planet Venus revolves around the sun at a distance of 108 million km in 228 earth days. Find its a) speed [34400 ms^-1]b) centripetal acceleration. [0.011 ms^-2]

2.14-2. A horisontal curve has the radius 140 m and the static friction coefficient is 0.09. At what maximum speed can a car take the curve without skidding? [11 ms^-1]

2.15-1. At what altitude above the surface of the earth (radius 6370 km) will the force of gravity on a 400 kg satellite be 20.0 N? [82855 km]

m16-1. Find the mass of earth if its radius is 6370 km and surface gravity acceleration 9.81 ms^-2. [5.97 x 10²⁴ kg]

2.16-2. A rocket is launched from the south pole to a stable orbit 600 km above the earth's surface. Find the energy that must be supplied by its rocket engine (assuming, unrealistically, that its mass of 15500 kg remains constant). [5.26 x 10¹¹ J]

2.16-3. Find a) the gravitational potential at the surface of a planet with the radius 3500 km and the gravity acceleration 7.70 ms^-2. [3.003 x 10⁷ Jkg^-1] b) the gravitational potential energy of a 15.5 ton flying saucer at that point. [-4.65 x 10¹¹ J]

2.17-1. If the planet in m16-3 had the escape speed 8.81 kms^-1, could it then have the surface gravity constant 7.70 ms^-2? [No, since the surface gravity acceleration should then be 11.1 ms^-2]

2.17-2. Estimate the size of an asteroid made of rock with the density 3000 kgm^-3, from whose surface you could throw a rock away into space. Estimate approximate values for necessary quantities. [Radius ca 15 km for a spherical asteriod if one can throw with 20 ms^-1, may vary depending on assumptions and methods]

2.18-1. Planet I has two moons, B and O. If B revolves around I in 55 earth days at a distance of 280 000 km, and O revolves around I in 68 earth days, find its distance from I. [ca 320 000 km]