ASRJC Physics Work, Energy and Power Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 5-1 Additional Notes Topic 5: Work, Energy and Power Content: A. Work B. Kinetic Energy and Potential Energy C. Conservation of Energy D. Power and Efficiency Learning Outcomes: Candidates should be able to: (a) define and use work done by a force as the product of the force and displacement in the direction of the force. (b) calculate the work done in a number of situations, including the work done by a gas which is expanding against a constant external pressure: W = pV. (To be discussed in First Law of Thermodynamics) (c) give examples of energy in different forms, its conversion and conservation, and apply the principle of energy conservation to simple examples. (d) show an appreciation for the implications of energy losses in practical devices and use the concept of efficiency to solve problems. (e) derive, from equations for uniformly accelerated motion in a straight line, the equation Ek = 1 2 mv2 (f) recall and use the equation Ek = 1 2 mv2. (g) distinguish between gravitational potential energy, electric potential energy and elastic potential energy. (h) deduce that the elastic potential energy in a deformed material is related to the area under the force-extension graph (i) show an understanding of, and use the relationship between force and potential energy in a uniform field to solve problems. (To be discussed in Gravitational Field) (j) derive, from the definition of work done by a force , the equation Ep = mgh for gravitational potential energy changes near the Earth’s surface. (k) recall and use the formula Ep = mgh for gravitational potential energy changes near the Earth’s surface. (l) define power as work done per unit time and derive power as the product of force and velocity in the direction of the force Name: _______________________________ ( ) Class: 25 / ____

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 5-2 Additional Notes Relating Science and Society There is heavy reliance on fossil fuels (e.g. crude oil, natural gas and petroleum products) for electricity generation in Singapore. It is important to capitalise on innovative ideas and technologies to promote the efficient use of energy, especially in the major sectors of energy use, namely power generation, industry, transport, buildings and households. It is also important to grow clean energy capabilities such as solar energy to reduce the dependence on fossil fuels. • Energy is the ability to do work; whereas work is the transfer of energy, or the process of converting energy. • When work is done, energy is transferred. A.1 Work Done by a Force • If a body moves as a result of a force being applied to it, the force is said to be doing work on the body. • When you exert a force F on an object making it move a displacement s in the direction of the force, your work done on the object, W is expressed as: • When the force and displacement are not in the same direction , we must use the component of the force which is parallel to the displacement. where  is the angle between the force and the displacement. • The unit for work is the Joule (J). • Work is a scalar quantity; it has only magnitude and no direction. • Work done can be positive (object gains energy) or negative (object loses energy). A Work Definition: The work done by a force is the product of the force and the displacement in the direction of the force. F s s θ F W = Fs W = (component of F in direction of s) × s = (F cos θ) × s = Fs cos θ Note: 1. To use these expressions for calculation, the force has to be constant. Otherwise, we will use area under Force− displacement graph, to be discussed in A.2. 2. We can also resolve displacement in the direction of the force and the expression for work done is still the same. Memorise

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 5-3 Additional Notes • The work done by a force is negative if the applied force has a component in a direction opposite to the displacement. e.g. work done by friction. • When the displacement of the object is perpendicular to the line of action of the force, the work done on an object is zero. Example 1 A boy pulls a 70 kg crate 40 m along a horizontal floor with a constant force of 100 N, which acts at an angle of 37° as shown below. The floor is rough and exerts a frictional force of 50 N. Determine (a) the work done by each force acting on the crate, and (b) the net work done on the crate Solution 37° 100 N 40 m 50 N Thinking Process: - What are the all the forces acting on the crate? Are there additional forces present that are not stated by the question? - Is the question asking for net work done or work done by each force? - Is net force / each force parallel to displacement? - If net force / each force is not parallel to displacement, what do we need to do to find work done? The sign of work done on the object determines whether the object gains or loses energy. It does not refer to direction as work done is a scalar quantity. When the work done by friction on a moving car is −700 J, this means that the car loses 700 J of energy, and 700 J of work is done against friction.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 5-4 Additional Notes A.2 Graphical Method for Determining Work Done by a Varying Force Work done by a Force • When the force varies with respect to the displacement, the work done is represented by the area enclosed under the Force−displacement graph. • Recall, from the topic Forces, the Force−extension diagram for an elastic object that obeys Hooke’s Law. • The elastic potential energy stored in the elastic object is a result of work done by the force and is given by area under the graph. • In this case, the work done, or elastic potential energy stored, is Work done = ½ F1 x1 = ½ (k x1) x1 = ½ k x12 where k is the spring constant. • In the case where the force applied is constant, and in the direction of the displacement, the work done is simply Fs. W = 2 1 s s F ds i.e. area under the Force−displacement graph. Force, F W displacement, s s2 0 s1 extension, x / m Force, F / N x1 F1 extension, x / m Force, F / N s F Do not confuse area under Force−displacement graph with area under Force−time graph. The former represents work done, while the latter represents impulse, i.e. change in momentum.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 5-5 Additional Notes Check Your Understanding 1 The force on a particle varies as shown in the figure below. Determine the work done by this force to move the particle along the axis from x = 0.0 m to x = 15.0 m. A 700 J B 2100 J C 2800 J D 3500 J Solution x / m F/ N 5 10 15 −200 −100 0 100 200 300 400

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 5-6 Additional Notes Ek = ½ mv2 B.1 Kinetic Energy • A body of mass m moving with velocity v possesses kinetic energy Ek given by • The SI unit for kinetic energy is the Joule (J). • Kinetic energy is a positive, scalar quantity. • Note that kinetic energy is independent of the way in which the body acquired this velocity (i.e. regardless of how it obtained its velocity). • The kinetic energy of an object can also be expressed in terms of its momentum. 2 2 2 2 k 1 m v pE = mv = =2 2m 2m • This expression is useful when we