1.
Which of the following is not a unit of work?
Correct Answer
C. Kilogram-meter
Explanation
A unit of work measures the amount of energy transferred when a force is applied over a distance. The newton-meter (also known as joule), joule, and watt-hour are all units of work because they represent the product of a force and a distance. However, kilogram-meter is not a unit of work because it represents the product of mass and distance, not force and distance.
2.
An object at rest may have
Correct Answer
D. Potential energy
Explanation
An object at rest may have potential energy because potential energy is the energy possessed by an object due to its position or condition. Even though the object is not moving, it can still have potential energy if it is in a position where it can potentially do work or has the potential to be converted into other forms of energy. Therefore, an object at rest can store potential energy.
3.
A moving object must have which one or more of the following?
Correct Answer
E. B,c,d
Explanation
A moving object must have kinetic energy, which is the energy possessed by an object due to its motion. It also must have rest energy, which is the energy an object possesses even when it is not in motion. Additionally, a moving object must have momentum, which is the product of its mass and velocity. Therefore, the correct answer is b,c,d, as all of these options are necessary for a moving object.
4.
When the momentum of a moving object is increased, there must also be an increase in which one or more of the following of the object's properties?
Correct Answer
E. A,c
Explanation
When the momentum of a moving object is increased, there must also be an increase in the object's speed and kinetic energy. This is because momentum is directly proportional to both mass and velocity. Therefore, if the momentum increases, either the mass or the velocity or both must increase. Since speed is directly related to velocity, an increase in momentum implies an increase in speed. Additionally, kinetic energy is directly proportional to mass and the square of velocity, so an increase in momentum implies an increase in kinetic energy as well.
5.
The total amount of energy (including the rest energy of matter) in the universe
Correct Answer
A. Cannot change
Explanation
The total amount of energy in the universe cannot change because of the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. This means that while energy can be converted from one type to another, the total amount of energy in the universe remains constant. Therefore, the correct answer is that the total amount of energy in the universe cannot change.
6.
When the speed of a moving object is halved,
Correct Answer
D. Its momentum is halved
Explanation
When the speed of a moving object is halved, its momentum is halved. Momentum is the product of an object's mass and its velocity. If the speed is halved, the velocity is also halved, resulting in a decrease in momentum.
7.
Two ball, one of mass 5 kg and the other of mass 10 kg, are dropped simultaneously from a window. When they are 1 m above the ground, the balls have the same
Correct Answer
D. Acceleration
Explanation
When the balls are 1 m above the ground, they have the same acceleration. This is because the acceleration due to gravity is constant for all objects near the Earth's surface. The mass of the objects does not affect their acceleration in free fall. Therefore, both balls will experience the same acceleration as they fall towards the ground, regardless of their mass.
8.
A bomb dropped from an airplane explodes in midair.
Correct Answer
A. Its total kinetic energy increases
Explanation
When a bomb dropped from an airplane explodes in midair, its total kinetic energy increases. This is because the explosion releases additional energy, adding to the bomb's initial kinetic energy. The explosion converts potential energy stored in the bomb into kinetic energy, causing an increase in the total kinetic energy of the system.
9.
The operation of a rocket is based upon
Correct Answer
C. Conservation of linear momentum
Explanation
The operation of a rocket is based on the principle of conservation of linear momentum. According to this principle, the total momentum of a system remains constant if no external forces act on it. In the case of a rocket, the expulsion of high-speed exhaust gases in one direction generates an equal and opposite force that propels the rocket forward. This is possible because the momentum of the expelled gases is transferred to the rocket, causing it to accelerate in the opposite direction. Therefore, the rocket's motion is governed by the conservation of linear momentum.
10.
A spinning skater whose arms are at her sides then stretches out her arms horizontally
Correct Answer
C. She spins more slowly
Explanation
When the skater stretches out her arms horizontally, she increases her moment of inertia. According to the law of conservation of angular momentum, the product of moment of inertia and angular velocity remains constant unless an external torque is applied. As the moment of inertia increases, the angular velocity must decrease to maintain the same angular momentum. Therefore, the skater spins more slowly when she stretches out her arms horizontally.
11.
According to the principle of relatively, the laws of physics are teh same in all frames of reference
Correct Answer
D. All of these
Explanation
The principle of relativity states that the laws of physics are the same in all frames of reference. This means that whether two frames of reference are at rest with respect to each other, moving toward or away from each other at a constant velocity, or moving parallel to each other at a constant velocity, the laws of physics will remain unchanged in each frame. Therefore, the correct answer is "all of these."
12.
The formula 1/2mv^2 for kinetic energy
Correct Answer
C. Is the low-speed approximation to the correct formula
Explanation
The formula 1/2mv^2 for kinetic energy is the low-speed approximation to the correct formula. This means that at low speeds, the formula provides a reasonably accurate estimate of the kinetic energy. However, at high speeds, the formula becomes less accurate and other factors such as relativistic effects need to be taken into account. Therefore, while the formula is correct for low speeds, it is only an approximation and not accurate for high-speed scenarios.
13.
A spacecraft has left the earth and is moving toward Mars. An observer on the earth finds that, relative to measurements made when the spacecraft was at rest, its
Correct Answer
A. Length is shorter
Explanation
As the spacecraft is moving toward Mars, it experiences time dilation and length contraction due to its high velocity. This means that, relative to measurements made when the spacecraft was at rest, its length appears shorter. This phenomenon is a consequence of special relativity, where objects moving at high speeds are observed to be contracted in the direction of their motion. Therefore, the correct answer is that the length of the spacecraft is shorter.
14.
The upper limit to the speed of an object with mass
Correct Answer
D. Is the speed of light
Explanation
The correct answer is "is the speed of light". According to Einstein's theory of relativity, the speed of light in a vacuum is the ultimate speed limit in the universe. No object with mass can reach or exceed the speed of light. As an object with mass approaches the speed of light, its kinetic energy increases, but it would require an infinite amount of energy to reach the speed of light itself. Therefore, the speed of light acts as an upper limit for the speed of an object with mass.
15.
It is not true that
Correct Answer
D. Momentum is a form of energy
Explanation
Momentum is not a form of energy. Momentum is a property of an object that depends on its mass and velocity, while energy is the ability to do work. Although momentum and energy are related concepts, they are not the same thing. Momentum is a vector quantity, meaning it has both magnitude and direction, while energy is a scalar quantity. Therefore, it is incorrect to say that momentum is a form of energy.
16.
Albert Einstein did not discover that
Correct Answer
B. The acceleration of gravity g is a universal constant
Explanation
The correct answer is "the acceleration of gravity g is a universal constant." Albert Einstein did not discover that the acceleration of gravity g is a universal constant. This concept was actually introduced by Isaac Newton in his law of universal gravitation. Einstein's theory of general relativity, on the other hand, described gravity as a warping of spacetime.
17.
The work done in holding a 50-kg object at a height of 2 m above the floor for 10 s is
Correct Answer
A. 0
Explanation
When an object is held at a certain height without any change in its position, the work done on the object is zero. This is because work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force. In this case, the force applied to hold the object at a height is equal to the weight of the object, which is mg, where m is the mass of the object and g is the acceleration due to gravity. However, since the displacement of the object is zero (no change in position), the work done is zero.
18.
The work done in lifting 30 kg of bricks to a height of 20 m is
Correct Answer
D. 5880 J
Explanation
The work done in lifting an object is calculated by multiplying the force applied to lift the object by the distance over which the object is lifted. In this case, the force required to lift the bricks is equal to their weight, which can be calculated using the formula weight = mass × gravity. Assuming a standard gravity of 9.8 m/s², the weight of 30 kg of bricks is 294 N. Multiplying this force by the distance of 20 m gives us a work done of 5880 J.
19.
A total of 4900 J is used to lift a 50 kg mass. The mass is raised to a height of
Correct Answer
A. 10 m
Explanation
The work done to lift an object is equal to the product of the force applied and the distance over which the force is applied. In this case, the work done is given as 4900 J. Since the force applied is equal to the weight of the object, which is given by the mass multiplied by the acceleration due to gravity, and the distance is given as 10 m, we can calculate the work done. By rearranging the equation for work, we can solve for the force applied, which is equal to the weight of the object. Dividing the work done by the force applied gives us the distance over which the force is applied, which is equal to the height the mass is raised to. Therefore, the correct answer is 10 m.
20.
The work a 300-W electric grinder can do in 5.0 min is
Correct Answer
D. 90 kJ
Explanation
The work done by an electric grinder can be calculated using the formula: work = power x time. In this case, the power is given as 300 W and the time is given as 5.0 min. To convert the time to seconds, we multiply by 60 (5.0 min x 60 s/min = 300 s). Therefore, the work done is 300 W x 300 s = 90,000 J = 90 kJ.
21.
A 150-kg yak has an average power output of 120 W. The yak can climb a mountain 1.2 km high in
Correct Answer
B. 4.1 h
Explanation
The yak has an average power output of 120 W. Power is defined as the work done per unit of time. The work done by the yak to climb the mountain is equal to the product of its weight and the height of the mountain. The work done can be calculated as 150 kg * 9.8 m/s^2 * 1200 m = 1,764,000 J. The time taken to do this work can be calculated using the formula power = work/time. Rearranging the formula, we get time = work/power. Substituting the values, we get time = 1,764,000 J / 120 W = 14,700 s. Converting this to hours, we get 14,700 s / 3600 s/h = 4.08 h, which is approximately 4.1 h.
22.
A 40-kg boy runs up a flight of stairs 4 m high in 4 s. His power output is
Correct Answer
B. 392 W
Explanation
The power output of an object is calculated by dividing the work done by the time taken. In this case, the work done is equal to the force applied (which is equal to the boy's weight) multiplied by the distance moved (which is the height of the stairs). The weight of the boy can be calculated using the formula weight = mass x gravity, where mass is 40 kg and gravity is approximately 9.8 m/s^2. Therefore, the work done is equal to (40 kg x 9.8 m/s^2) x 4 m = 1568 J. Since the time taken is 4 s, the power output is equal to 1568 J / 4 s = 392 W.
23.
Car A has a mass of 1000 kg and is moving at 60 km/h. Car B has a mass of 2000 kg and is moving at 30 km/h. The kinetic energy of Car A is
Correct Answer
C. Twice that of car B
Explanation
The kinetic energy of an object is given by the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity. In this case, Car A has a mass of 1000 kg and is moving at 60 km/h, while Car B has a mass of 2000 kg and is moving at 30 km/h. To compare their kinetic energies, we can calculate them using the formula. For Car A, KE = 1/2 * 1000 * (60/3.6)^2 = 500,000 J. For Car B, KE = 1/2 * 2000 * (30/3.6)^2 = 250,000 J. Therefore, the kinetic energy of Car A is twice that of Car B.
24.
A 1-kg object has a potential energy of 1 J relative to the ground when it is at a height of
Correct Answer
A. 0.102 m
Explanation
The potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. In this case, the mass of the object is 1 kg and the potential energy is 1 J. By rearranging the formula, we can solve for h: h = PE / (mg). Substituting the given values, we get h = 1 J / (1 kg * 9.8 m/s^2) = 0.102 m. Therefore, the object has a potential energy of 1 J relative to the ground when it is at a height of 0.102 m.
25.
A 1-kg object has kinetic energy of 1 J when its speed is
Correct Answer
C. 1.4 m/s
Explanation
The kinetic energy of an object is given by the formula KE = 1/2 mv^2, where m is the mass of the object and v is its velocity. In this case, we are given that the object has a mass of 1 kg and a kinetic energy of 1 J. By rearranging the formula, we can solve for v: v = sqrt(2KE/m). Plugging in the values, we get v = sqrt(2*1/1) = sqrt(2) ≈ 1.4 m/s. Therefore, the speed of the object is approximately 1.4 m/s.
26.
The 2-kg blade of an ax is moving at 60 m/s when it strikes a log. If the blade penetrates 2 cm into the log as its KE is turned into work, the average force it exerts is
Correct Answer
D. 180 kN
Explanation
When the blade of the ax strikes the log, its kinetic energy (KE) is converted into work done to penetrate the log. The work done is equal to the force applied multiplied by the distance penetrated. In this case, the distance penetrated is given as 2 cm, which is 0.02 m. The KE of the blade can be calculated using the formula KE = 0.5 * mass * velocity^2. Substituting the given values, KE = 0.5 * 2 kg * (60 m/s)^2 = 3600 J. The work done is equal to the KE, so the force applied can be calculated using the formula work = force * distance. Rearranging this formula, force = work / distance = 3600 J / 0.02 m = 180,000 N = 180 kN. Therefore, the average force exerted by the blade is 180 kN.
27.
A 1-kg ball is thown in the air. When it is 10 m above the ground, its speed is 3 m/s. At this time most of the ball's total energy is in the form of
Correct Answer
C. Rest energy
28.
A 10,000-kg freight car moving at 2 m/s collides with a stationary 15,000-kg freight car. The two cars couple together and move off at
Correct Answer
A. 0.8 m/s
Explanation
When the two freight cars collide, they experience a conservation of momentum. The momentum before the collision is equal to the momentum after the collision. The momentum of an object is given by the product of its mass and velocity. The initial momentum of the first freight car is (10,000 kg)(2 m/s) = 20,000 kg*m/s, and the initial momentum of the second freight car is (15,000 kg)(0 m/s) = 0 kg*m/s. After the collision, the two cars couple together and move off with a common velocity. Let's call this final velocity "v". The final momentum of the coupled cars is (10,000 kg + 15,000 kg)(v) = 25,000 kg*v. Since momentum is conserved, we can set the initial momentum equal to the final momentum: 20,000 kg*m/s + 0 kg*m/s = 25,000 kg*v. Solving for "v", we find that v = 0.8 m/s. Therefore, the correct answer is 0.8 m/s.
29.
A 30-kg girl and a 25-kg boy are standing on frictionless roller skates. The girl pushes the boy, who moves off at 1.0 m/s. The girl's speed is
Correct Answer
C. 0.83 m/s
Explanation
When the girl pushes the boy, according to Newton's third law of motion, an equal and opposite force is exerted on the girl. Since the boy moves off at 1.0 m/s, it means that the girl also moves in the opposite direction with the same speed. Therefore, the girl's speed is 1.0 m/s.
30.
An object has a rest energy of 1 J when its mass is
Correct Answer
A. 1.1 X 10^-17 kg
Explanation
The rest energy of an object is given by the equation E = mc^2, where E is the energy, m is the mass, and c is the speed of light. In this case, the rest energy is given as 1 J. Since the speed of light is a constant, the only variable that can affect the rest energy is the mass. Therefore, the object must have a mass of 1.1 X 10^-17 kg in order to have a rest energy of 1 J.
31.
The smallest part of the total energy of the ball of multiple choice 27 is
Correct Answer
A. Kinetic energy
Explanation
The smallest part of the total energy of the ball would be its kinetic energy. Kinetic energy is the energy possessed by an object due to its motion. In the context of the ball, it refers to the energy it has as it moves. Potential energy relative to the ground would be higher if the ball is at a higher position, rest energy refers to the energy an object possesses when it is at rest, and momentum refers to the quantity of motion an object has. Thus, kinetic energy is the smallest part of the total energy in this scenario.
32.
The lightest particle in an atom is an electron, whose rest mass is 9.1X10^-31 kg. The energy equivalent of this mass is approximately
Correct Answer
A. 10^-13 J
Explanation
The energy equivalent of the mass of an electron can be calculated using Einstein's famous equation, E = mc^2, where E is the energy, m is the mass, and c is the speed of light. Plugging in the given mass of the electron, we get E = (9.1X10^-31 kg)(3X10^8 m/s)^2 = 8.19X10^-14 J. Since this value is closest to 10^-13 J, the correct answer is 10^-13 J.