Testing Newton’s Second Law
ITQ2 ;PTL
P PP PPP P] :WLLK :WLLK :WLLK :WLLK ;PTL ;PTL ;PTL (i) (iii) (ii) (iv) ITQ3 1.23 m s–2
Chapter summary
• The rate at which distance is covered is called speed. Speed is a scalar quantity. • Acceleration is the rate at which either speed or velocity changes with time. • Acceleration could be either a scalar or a vector quantity: a scalar quantity if it is
derived from speed, or a vector quantity if derived from velocity.
• The displacement of a body is the change of its position from its starting point. It has direction and is, therefore, a vector quantity.
• Velocity is the rate of change of displacement with time. It is a vector quantity. • Speed–time and velocity–time graphs can be used to solve problems on straight-line
motion.
• Newton formulated three laws that can be used to study motion:
– Newton’s First Law can be used to study motion under no external force. – Newton’s Second Law is concerned with motion under an unbalanced force. – Newton’s Third Law is concerned with the relationship between forces that come
into play to cause momentum to change.
• Momentum is defined as mass × velocity. Its symbol is p and its S.I. unit is kg m s–1.
ITQ4 (a) 0 3 3 + t 10 m 0 Time, t/s V elocity , v
(b) 0 3 3 + t 10 m 0 Time, t/s Speed, v (c) 3 3 + t 0 Time, t/s AccelerationITQ5 If we don’t pedal the bike will slow down because of friction from the road at the axles and from the wind. A force therefore has to be used to overcome these resistive forces and bring the unbalanced force to zero.
ITQ6 10 m s–1 in the direction of the force.
ITQ7 The newton is that force which will give to a mass of 1 kg an acceleration of 1 m s–2.
ITQ8 As the athlete moves lower on the trampoline, he encounters greater resistance from the extended springs. This resistive force slows the athlete down. This illustrates the second law: the external resistive force from the springs acts to reduce the momentum of the athlete. Third Law: on hitting the trampoline, the impact (shock) produced by the athlete on the trampoline on landing acts downward on the trampoline and the trampoline exerts an equal and upward shock on the athlete.
ITQ9 It is safer to use a soft trampoline because the springs, being softer, do not exert such a large retarding force the on the athlete and the athlete comes to rest more slowly. The ‘jolt’ felt by the ankles and knees is therefore less and so the likelihood of sustaining injury is thereby reduced.
Examination-style questions
(Where necessary, take the acceleration due to gravity to be 10 m s–2.)
1 A passenger paces up and down in a stationary aircraft in a straight line at 0.50 m s–1,
covering a distance of 10 m at a time in each direction.
(i) Assuming that he paces up and down 5½ times before stopping, for his motion draw: (a) a speed–time graph;
(b) a velocity–time graph; (c) a distance–time graph; (d) a displacement–time graph.
2 The velocity–time graph below represents the motion of a ball falling then rebounding in a vertical line. 0 Time/s Velocity/m s–1 3 –2 (i) Find:
(a) the time of fall of the ball; (b) the time of rise of the ball; (c) the total distance covered;
(d) the overall displacement of the ball.
(ii) Describe the motion of the ball and sketch a displacement–time graph to represent this motion.
3 A motor-bike under test accelerates uniformly from rest and moves in a straight line. In 3 seconds it reaches a speed of 40 m s–1. It then travels at this speed for 10 seconds, and
then brakes to a stop in a further 2 seconds.
(i) (a) Draw a speed–time graph to represent the motion of the motor-bike. (b) Calculate the total distance the bike travels over the period of the trial. (c) Calculate the average speed of the bike over the period of the trial.
(ii) If the bike were to accelerate for a period and, straight after this, begin to brake in such a way that it braked over the same time as it accelerated, what would be the acceleration? Assume the test distance and duration are the same as in the first case. 4 A boy of mass 50 kg lets himself down out of a tree, falling from rest through a distance of
4 m. He brings himself to rest 0.5 second after his feet first touch the ground. (i) Calculate:
(a) his velocity on touching the ground; (b) his change in momentum in coming to rest;
(c) the force exerted by the ground in bringing the boy to rest; (d) the boy’s average deceleration as he is brought to rest.
(ii) Explain why, in falling from a great height, it is always a good idea to ‘break your fall’ either by choosing to fall on soft ground (if you can), or to take as long as possible to come to rest.
5 State and explain what is liable to happen when you: (i) step off a chair that is standing on a smooth floor;
(ii) press against a wall with your palms, standing on a smooth floor in shoes with smooth soles;
6 Explain the following:
(i) the action of moving a boat forwards by using a paddle;
(ii) the use of a loop of rope around your ankles when climbing a tall, practically straight, tree (such as a coconut tree) without branches;
(iii) why a humming bird can remain at rest by flapping its wings at a certain rate. 7 A steel ball of mass 0.50 kg falls from rest from a height of 2.0 m on to firm ground.
(i) Find, by using a velocity–time graph: (a) how long it takes to reach the ground; (b) its velocity on touching the ground.
(ii) On the ground, the ball comes to rest in 0.01 s. Calculate: (a) the deceleration of the ball;
(b) how far the ball penetrates into the ground.
(iii) Sketch a velocity–time graph for the entire motion of the ball.
8 When jumping on to the ground from a height, landing after parachuting, or skiing over bumpy ground, people are often told: ‘Bend your knees or break your legs.’ Use your knowledge of physics to explain why.
understand why energy is defi ned as the ‘ability to do work’ or the ‘capacity fordoing work’
defi ne work done by and work done against a force distinguish between potential energy and kinetic energy use the formula for the change of potential energy of an object to solveproblems
use the formula for the kinetic energy of an object to solve problems use the principle (or law) of conservation of energy to solve problems defi ne power and use the defi nition to solve problems understand the meaning and the signifi cance of the term ‘effi ciency’ calculate effi ciency in a given situation name some alternative sources of energy in the Caribbean and discussthe feasibility and importance of each of these sources as an alternative to conventional ones
elastic chemical electrical magnetic
POTENTIAL – condition, state or position MECHANICAL
sources secondary
primary
ENERGY WORK force × displacement
capacity to do work = =
KINETIC – motion nuclear
gravitational
fossil wind waves water nuclear geothermal the Sun coal, oil, gas windmills rocking boom renewable sources non-renewable sources waterfalls, dams uranium solar panels, solar cells, solar furnaces
Introduction
Most of us would agree that, if we didn’t eat, we would soon become very frail and feel very weak. We would say that we lacked energy. Our muscles would
By the end of this chapter you should be able to: