physics KE and PE

Formula for Potential Energy

PE= mghi

Formula for Conservation

PEi + KEi = PEf + KE mghi + ½ mvi2 = mghf + ½ mvf2

T OR F: Gravitational potential energy is lost as objects free-fall to the ground.

TRUE - As objects free-fall, the height (h) decreases; subsequently, the PE decreases.

T OR F: If an object is at rest, then it does not have any kinetic energy.

TRUE - Kinetic energy depends upon speed. If there is no speed (the object is at rest), then there is no kinetic energy.

T OR F: Kinetic energy is a scalar quantity.

TRUE - Kinetic energy does not have a direction associated with it; it is a scalar quantity.

T OR F: An object can never have a negative kinetic energy.

TRUE - Kinetic energy is determined by the equation 0.5•m•v2. the quantity m is always positive. And even if v is negative, v2 will always be positive. Therefore, kinetic energy can never be a negative value.

T OR F: An object has a kinetic energy of 40 J. If its mass were twice as much, then its kinetic energy would be 80 J.

TRUE - Kinetic energy is directly related to the mass of an object.

T OR F: The unit of measurement for potential energy is the Joule.

TRUE - The Joule (abbrev. J) is the standard metric unit of energy - all forms of energy.

T OR F: The gravitational potential energy of an object is dependent upon the mass of the object.

TRUE - The equation states that PEgrav = m•g•h; PE is dependent upon mass.

T OR F: The higher that an object is, the more potential energy which it will have.

TRUE - The equation states that PEgrav = m•g•h; PE is directly related to height.

T OR F: If the mass of an elevated object is doubled, then its gravitational potential energy will be doubled as well.

TRUE - The equation states that PEgrav = m•g•h; if the m is doubled, then the PE will be doubled as well.

T OR F: Potential energy is the energy stored in an object due to its position.

TRUE - This is the definition of potential energy.

QUESTION: A 75 kg boy is skiing down a slope from a height of 25 m with an initial speed of 12.0 m/s. What is his speed at the bottom of the slope?

vf = 25.19 m/s

QUESTION: A student rides a bicycle up a 30 degree hill at a constant speed of 6 m/s. The combined mass of the student and the bicycle is 70 kg. What is the kinetic energy of the student-bicycle system during this ride?

1260 J

QUESTION: A spring has a spring constant of 120 N/m. How much potential energy is stored in the spring as it is stretched 0.20 m? a) 2.4 J b) 4.8 J c) 12 J d) 24 J

A - PEe = 1/2kx2 = 2.4 J

QUESTION: When a spring is stretched 0.200 m from its equilibrium position, it possesses a potential energy of 10 J. What is the spring constant for this spring? a) 100 N/m b) 125 N/m c) 250 N/m d) 500 N/m

D - PEe = 1/2kx2 k = 2PEe/x2 = 500 N/m

QUESTION:As the speed of a bicycle moving along a level horizontal surface changes from 2 m/s to 4 m/s, the magnitude of the bicycle's gravitational potential energy: a) decreases b) increases c) stays the same.

C - the height is not changing because it is on a flat surface - therefore PE does not change

QUESTION: As an object falls freely near the Earth's surface, the loss of gravitational potential energy of the object is equal to a) gain in speed b) loss of mass c) gain in kinetic energy d) loss of height e) loss of kinetic energy

C - total mechanical energy is conserved so change in PE equals change in KE

T OR F: The kinetic energy of an object is dependent upon the weight and the speed of an object.

FALSE (sort of) - Kinetic energy depends upon mass and speed. Two objects of the same mass could have different weights if in a different gravitational field; so it is not appropriate to say that kinetic energy depends upon weight.

T OR F: Faster moving objects always have a greater kinetic energy.

FALSE - Faster moving objects would have more kinetic energy than other objects of the same mass. However, another object could have less speed and make up for this lack of speed in terms of a greater mass.

T OR F: Both gravitational and elastic potential energy are dependent upon the mass of an object.

FALSE - Gravitational potential energy is dependent upon the mass of the object (PEgrav = m•g•h) but elastic potential energy is dependent upon the spring constant and the compression or stretch length of the spring (PEelastic = 0.5•k•x2).

T OR F: A falling object always gains kinetic energy as it falls

FALSE - If an object is falling at a constant velocity (i.e., the air resistance force equals the downward force of gravity), then there is not an increase in kinetic energy. It is true however that free-falling objects always increase their kinetic energy as they fall.

If an object is on the ground, then it does not have any kinetic energy.

FALSE - If an object is on the ground, then it does not have potential energy (relative to the ground).

T OR F: Kinetic energy is the form of mechanical energy which depends upon the position of an object.

FALSE - Kinetic energy depends upon the speed of the object; potential energy depends upon the position of the object.

T OR F: An object has a kinetic energy of 40 J. If its speed were twice as much, then its kinetic energy would be 80 J.

FALSE - Kinetic energy is directly related to the square of the speed of an object. So a doubling of the speed would result in a quadrupling of the kinetic energy - the new KE would be 160 J.

T OR F: More massive objects always have a greater kinetic energy.

FALSE - More massive objects would have more kinetic energy than other objects with the same speed. However, another object could have less mass and make up for this lack of mass in terms of a greater speed.

T OR F: Moving objects cannot have potential energy.

FALSE - Potential energy has nothing to do with speed; an object could be moving at an evated poselition. It is this elevation above zero level which gives an object potential energy.

T OR F: If work is done on an object by a non-conservative force, then the object will either gain or lose kinetic energy.

FALSE - Such an object will definitely gain or lose mechanical energy but not necessarily kinetic energy.

T OR F: A 1-kg mass at a height of 1 meter has a potential energy of 1 Joule.

FALSE - The final potential energy is calculated as PE = m•g•h = (1 kg)•(~10 m/s/s)•(1 m) = ~10 J.

T OR F: A 1-kg object falls from a height of 10 m to a height of 6 m. The final potential energy of the object is approximately 40 J.

FALSE - The final potential energy is calculated as PE = m•g•h = (1 kg)•(~10 m/s/s)•(6 m) = ~60 J; the loss in potential energy during this 4-m fall is -40 J.

T OR F: A 1-kg object is accelerated from rest to a speed of 2.0 m/s. This object gains 4.0 Joules of kinetic energy.

FALSE - The kinetic energy increases from 0 J to 2 J (0.5•1•22); that's an increase by 2 J.

T OR F: If work is done on an object by a non-conservative force, then the object will either gain or lose potential energy.

FALSE - The object will either gain or lose mechanical energy, but not necessarily potential energy.

T OR F: Object A has a mass of 1 kg and a speed of 2 m/s. Object B has a mass of 2 kg and a speed of 1 m/s. Objects A and B have the same kinetic energy.

FALSE - When it comes to kinetic energy, speed is doubly important (recall v2). So in this case, object A would have more kinetic energy. Doing the calculation yields 2 J for object A and 1 J for object B.

Formula for Kinetic Energy

KE= ½ mv^2