FACULTY OF EDUCATION Department of Curriculum and Pedagogy

FACULTY OF EDUCATION Department of Curriculum and Pedagogy Physics Weight and Mass Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement Fund 2012 -2013

Weight and. Title Mass Question

Conventions Question Title Units: In this question set we will use kilograms (kg) to describe mass. Weight/Force will be discussed in terms of pounds (lbs), the more commonly used Imperial unit.

SI (metric) and Imperial Question Title Systems of Measurement International System of Units (SI) • Length: – Meter, Centimetre, Millimetre, Kilometre • Mass: – Milligram, Gram, Kilogram, Metric Ton • Force: – Newton, Kilonewton • Time: – millisecond, minute, hour Imperial System of Units • Length: – Inch, Foot, Mile • Mass: – Slug • Force: – Pound • Time: – millisecond minute hour

Mass I Question Title Suppose a one kilogram (kg) gold bar is made up of exactly one billion identical particles. Is there a way to assemble any other number of gold particles to form a 1 kg gold bar? A. Yes, but only if the particles are moved to a different location. B. Yes, but we must change the shape of the object. A. No, it is not possible. B. Yes, but we must change both the object’s shape and location.

Solution Question Title Answer: C Justification: Mass can be thought of as a fundamental property of an object, similar to length. If a similar question was asked regarding a rope of length 1 m comprised of 10 smaller equally sized bits, the answer would be the same. Like length, the only way to change an object’s mass is to take some away (remove a piece of rope) or add matter (add an 11 th piece of rope). 1 m

Mass II Title Question Imagine you are editing a fictional universe in a computer game, when you accidently delete everything except for a 5 kg block. If the block is now the only object in the universe, what is the mass of the block? A. The computer game won’t be able to calculate a mass. B. The new mass is less than 5 kg. C. The new mass is more than 5 kg. D. The new mass is exactly 5 kg.

Solution Question Title Answer: D Justification: As we discovered in the last question, mass is a fundamental property of an object. An object’s mass is entirely independent of its environment. In terms of environment, mass can be thought of in a way similar to length; a 1 m length of rope is always 1 m long regardless of where it is. Mass, like length, does not depend on its surroundings.

Mass III Title Question There are two hockey players standing on the ice, one is 140 kg and the other is 70 kg. If you had to collide with one of the hockey players, which would have a smaller impact on you? Mass: 140 kg Mass: 70 kg A. The big one because he is more massive. C. The small one because he is less massive. B. Always the one whose mass is closest to mine. D. The impact of the collisions is the same.

Solution Question Title Answer: C Justification: The reason why we choose the smaller hockey player is because he is less massive. The mass of an object determines how much the object will resist changes in its speed or direction of motion. If you collide with the heavy hockey player his mass will resist being moved more than the lighter hockey player. Therefore, by colliding with the hockey player with less resistance to changes in motion, the impact of the collision is minimized for you.

Mosquito Raindrop Question Vs. Title

Mass IV Title Question The mass of an object describes how much it will resist changes to its speed or direction of motion. Which of the following statements describes this phenomenon? 1. When a car takes a sharp turn to the right, the driver feels pushed to the left against the car door. The more massive the driver, the greater the force exerted on the driver by the door and vice versa. 2. It is harder to push a monster truck than a smart car. 3. It is more difficult to hold a 50 kg box above your head than a 25 kg box. A. 1, 3 B. 2, 3 C. 1, 2 D. 1, 2, 3

Solution Question Title Answer: C Justification: The correct answer is C because statements 1 and 2 describe changing an object’s speed or direction of motion. In statement one the individual feels a force because the door of the car must push the person to change the direction of their motion. If it were not for the door the passenger would continue in the original direction of the car. The heavier the person, the more they will resist the change in motion and thus the door will have to push harder to make the individual’s trajectory match that of the car. The second statement involves changing the position and speed of stationary vehicles. Because the monster truck is more massive than the smart car, it is harder to get moving. Solution is continued on next slide

Solution Question Title Answer three is not correct because it does not demonstrate a change in the speed or direction of an object’s movement. To hold 50 kg of mass above our heads we must continually fight the attractive interaction between the objects mass and the Earth, otherwise known as the force of gravity, or the object’s weight. We are holding the mass in a stationary, constant position.

Resource-Gravity/Weight Question Title

Weight I Title Question The force of gravity between two masses is proportional to the product of the masses. Which pair of objects has the greatest gravitational attraction? A. B. C. 100 kg 5 kg 15 kg 2 kg 5 kg 15 kg

Solution Question Title Answer: C Justification: In A, 100 x 2 = 200 In B, 5 x 5 = 25 In C, 15 x 15 = 225 The force of gravity is strongest in case C because the product is greater than any other combination of masses. This force is what we refer to when discussing weight.

Weight II Title Question The force of gravity between two masses is dependent on the distance between two objects. The farther apart the objects are, the less they attract one another. Which set of objects has the greatest gravitational attraction? A. 5 kg B. 5 kg C. 5 kg

Solution Question Title Answer: A Justification: The masses of all of the objects are the same, therefore the strength of the gravitational attraction relies only on the distance between the objects. The closer the pair, the stronger the gravitational attraction. The objects in case A are closer together than the other two options.

Weight III Title Question Weight is another word for gravitational force. The mass of the Earth is 81 times the mass of the Moon. In which situation does the 5 kg block weigh the most? A. C. 5 kg 100 km B. 5 kg 100 km 5 kg

Solution Question Title Answer: B Justification: In A and C the masses are the same distance apart however the masses in A have a smaller product than in C. B and C have the same product of masses however, the block in B is closer to the Earth resulting in a stronger gravitational force.

Weight IV Title Question Weight of an object is represented by the gravitational interaction between an object and its closest planet. The force of gravity exerted on one kilogram object on the Moon is one sixth of the force of gravity exerted on the same object on Earth. What is the ratio of the mass of a pound of gold on the Moon to a pound of gold on the Earth? A. 2: 12 B. 6: 1 C. 1: 1 D. 1: 6 E. A & D

Solution Question Title Answer: B Justification: If the force of gravity on 1 kg on the Moon is one sixth of what it is on the Earth, then the weight of 1 kg of mass on the Moon is also one sixth of what it is on Earth. If we recognize a pound as a unit of weight than we can reason that we would need six times as much mass on the Moon in order for the force exerted on the two objects to be the same. If 1 kg on the Moon has 1/6 th the weight of 1 kg on Earth then 6 kg on the Moon has the weight of 1 kg on Earth. In order to get the ratio right, we must consider the order. Because the question ask for the ratio of Moon to Earth it is important that our ratio follows the same order of Moon : Earth (6: 1).

Weight V Title Question Imagine you are editing a fictional universe in a computer game, when you accidentally delete everything except for a 5 pound block. If the block is now the only object in the universe, what is the weight of the block? A. The computer game won’t be able to calculate its weight. B. The new weight will be less than 5 pounds. C. The new weight will be more than 5 pounds. D. The new weight is 5 pounds.

Solution Question Title Answer: A Justification: Unlike mass, weight is not a fundamental property of an object. Rather it is an interaction between an object and its surroundings. If there is one object in the entire universe, then the concept of weight is meaningless because there is nothing else for the object to interact with. If we remember from the previous questions, weight is dependent on the two masses and the distance between them. If there are not two objects, the computer game would be unable to calculate the weight of the solitary mass.

Weight VI Title Question What weighs more, a kilogram of feathers or a kilogram of rice? A. The kilogram of rice B. The kilogram of feathers C. They weigh exactly the same D. Not enough information.

Solution Question Title Answer: D Justification: The question doesn’t specify the objects’ location. The feathers could be on a different planet than the rice, which would result in radically different weights for the two kilograms of mass. Because weight is dependent on the distance between two masses and the mass of the planet nearest the object, the location of the objects is important information.

Weight VII Title Question If a pound of rice and a pound of feathers are on the same planet, which contains more mass? A. The pound of rice B. The pound of feathers C. They have exactly the same mass D. Not enough information.

Solution Question Title Answer: D Justification: This question is extremely similar to the last. Weight is dependent on both location and mass, therefore if the location is not given we cannot assume the two lb’s correspond to the same mass. A pound rice and a pound of feathers will contain approximately the same mass if they are on the same planet. However, unless the exact position is given, they will not be exactly the same mass. The force of gravity on Earth is the strongest in Oslo (Norway) and the weakest in Mexico City (Mexico). These differences are not big enough to impact most people, but scientists and engineers must use the regional values for their calculations.

Weight and Mass I Comments Two people are racing to see who can push a semi-truck 100 m along frictionless rails the fastest. Both racers are given the same rails and same truck, however, one is on the Moon and the other is on Earth (inside a vacuum). Which racer has the advantage? A. The person on the Moon B. The person on Earth C. No advantage.

Solution Question Title Answer: C Justification: When pushing an object along a frictionless surface, the weight of the object doesn’t affect how hard it is to accelerate the object. This is because the force of gravity is acting directly down towards the center of the Earth, which doesn’t act against any of the horizontal force the racers apply to the trucks. The only thing resisting the acceleration of the racers is the mass of the trucks. Even though the truck on the Moon weighs six times less than the truck on the Earth, the masses are the same, therefore there is no advantage.

Weight and Mass II Comments Two people want to see who can hold the most mass over their heads for the longest amount of time. One is on Earth, and one is on the Moon. Which lifter has the advantage? A. The person on the Moon B. The person on Earth C. No advantage.

Solution Question Title Answer: A Justification: The weight of the object is what makes it difficult to lift heavy things. When the weight lifters are holding the weights above their heads, they are exerting a force on them equal in magnitude to their weight. To stop the weights from falling back to the ground, the weight lifters must push as hard up as the gravity is pulling down.

Weight and Mass III Comments If the bottom string is pulled with a gradually increasing force that eventually exceeds the breaking point of the string, which string will break and why? A. The top string will break because of the ball’s mass. C. The top string will break because of the ball’s weight. CLICK HERE FOR VIDEO! B. The bottom string will break because of the ball’s mass. D. The bottom string will break because of the ball’s weight.

Solution Question Title Answer: C Justification: The top string will break because of the weight of the ball. This is because, in addition to the tension caused by pulling the bottom string, the force of gravity acting on the ball increases the tension in the top string, but does not effect the bottom string. Therefore the tension in the top string reaches the breaking point first. Top string Bottom string

Weight and Mass IV Comments If the bottom string is pulled extremely hard and very suddenly, which string will break and why? A. The top string will break because of the ball’s mass. C. The top string will break because of the ball’s weight. CLICK HERE FOR VIDEO B. The bottom string will break because of the ball’s mass. D. The bottom string will break because of the ball’s weight.

Solution Question Title Answer: B Justification: The bottom string will break first because of the mass of the ball. If we try to accelerate the ball quickly, the ball’s resistance to movement (mass) will create a tension force in the bottom string greater than the top string. If the attempted acceleration (speed of the pull) is fast enough, the force required to move the ball will exceed the tension the string can withstand. Top string Bottom string

Resource Demonstration Question -Title