Question 1

Negative work can be done

Accepted Answer

Option (a) describes friction on the tires while a car is accelerating without skidding. This would result in positive work being done by the frictional force, as the force is in the same direction as the displacement of the car. 
Option (b) describes a spring at the bottom of an elevator shaft that stops a falling elevator. In this case, the spring would initially be compressed due to the motion of the elevator, and as it comes to a stop, the force exerted by the spring would be in the opposite direction to the motion of the elevator. This would result in negative work being done by the spring. 
Option (c) describes a hand catching a ball. In this case, as the hand catches the ball, the hand must exert a force on the ball in the opposite direction to its motion, in order to bring it to a stop. This would result in negative work being done by the hand. 
Therefore, only options (b) and (c) describe situations where negative work is done.

Question 2

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their speeds at the instant of launch is

Accepted Answer

The answer of Two clowns are launched from the same...

Question 3

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μ_k,then dragged back along the same path to its original position,the work done by friction is

Accepted Answer

The work done by friction over the entire round trip is negative because friction always opposes the motion, and it is doubled because the crate is dragged the same distance in both directions. The work done by friction in one direction is $-\mu_k mgd$, so for the round trip, it is $-2\mu_k mgd$.

Question 4

In a contest,two tractors pull two identical blocks of stone the same distance over identical surfaces.However,block A is moving twice as fast as block B when it crosses the finish line.Which statement is correct?

Accepted Answer

The answer of In a contest,two tractors pull two identical...

Question 5

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their kinetic energies at the instant of launch is

Accepted Answer

The kinetic energy of an object is given by K= 0.5mv^2, where m is the mass of the object and v is its velocity. Since both clowns are launched from the same cannon with the same spring compression, they both have the same initial velocity. Therefore, the kinetic energy depends only on their masses. Kinetic energy is directly proportional to the mass of the object. The relation between the kinetic energies of Clown A and Clown B is given by: KA/KB= (0.5 x 40 x v^2)/(0.5 x 60 x v^2) KA/KB= (40/60) KA/KB= (2/3) KA= (2/3)KB This means that the kinetic energy of Clown A is two-thirds of that of Clown B, or in other words, the kinetic energies of the two clowns are in the ratio of 2:3. This can be simplified to: KA/KB = 2:3 or KA/K_A = KB/K_B which is the same as choice C.

Question 6

When a ball rises vertically to a height h and returns to its original point of projection,the work done by the gravitational force is

Accepted Answer

Work done by a force is given by the dot product of the force and the displacement of the object in the direction of the force. In this case, the gravitational force is acting opposite to the displacement of the ball as it rises and falls. Therefore, the work done by the gravitational force is negative during both the upward and downward motion. However, since the displacement of the ball is zero from its initial position to its final position, the net work done by the gravitational force is zero.

Question 7

Planets go around the sun in elliptical orbits.The highly exaggerated diagram below shows a portion of such an orbit and the force on the planet at one position along that orbit.The planet is moving to the right.F_|| and Are the components of the force parallel (tangential)and perpendicular (normal)to the orbit.The work they do is W_|| and )At the position shown

Accepted Answer

The answer of Planets go around the sun in elliptical...

Question 8

A mass attached to the end of a spring is pulled out and released on a surface with friction.The work 
Done on the mass by the force exerted by the spring

Accepted Answer

During one half of each cycle, the force exerted by the spring is in the opposite direction to the displacement of the mass, so the work done on the mass by the spring force is negative. During the other half of each cycle, the force exerted by the spring is in the same direction as the displacement of the mass, so the work done on the mass by the spring force is positive. The change in energy owing to friction is always negative (energy is lost to the surroundings), so during the first half of each cycle, the work done by the spring force has the same sign as the change in energy owing to friction, and during the second half of each cycle, the work done by the spring force has the opposite sign as the change in energy owing to friction. Therefore, C is the correct choice.

Question 9

If the scalar (dot)product of two vectors is negative,it means that

Accepted Answer

The scalar (dot) product of two vectors is negative when the angle between them is between 90 and 180 degrees, indicating that the vectors are pointing in more opposite than the same direction.

Question 10

A 30-kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s.While she remains seated in the same spot and travels in a circle,the work the seat performs on her in one complete rotation is

Accepted Answer

The work done by a force is given by the formula W = Fdcosθ, where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors. In this case, the force exerted by the seat on the child is directed towards the center of the merry-go-round, but the displacement of the child is tangential to the circular path. Therefore, θ = 90° and cosθ = 0, which means that no work is done by the seat on the child. The correct answer is (A) 0 J.

Question 11

Two cannonballs are dropped from a second floor physics lab at height h above the ground.Ball B has four times the mass of ball A.When the balls pass the bottom of a first floor window at height Above the ground,the relation between their kinetic energies,K_A and K_B,is

Accepted Answer

The answer of Two cannonballs are dropped from a second...

Question 12

Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A,and a constant force 2F is applied to B.The relative amounts of work done by the two forces are related by

Accepted Answer

The work done by a force is equal to the product of the force and the displacement, W = F * d. Since carts A and B have equal masses and travel equal distances, the displacement is the same. Therefore, the amount of work done is proportional to the applied force. The ratio of the work done by the two forces is 2F/F = 2. Therefore, the relative amounts of work done by the two forces are related by W_B = 2 W_A.

Question 13

The work 
Done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d 
Is

Accepted Answer

The answer of The work 
Done by the force exerted...

Question 14

Two balls,A and B,of mass m and 2m respectively,are carried to height h at constant velocity,but B rises twice as fast as A.The work the gravitational force does on B is

Accepted Answer

The answer of Two balls,A and B,of mass m and...

Question 15

Sally,who weighs 450 N,stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street.He applies a constant 100 N force.

Accepted Answer

Work is calculated as the product of the force applied in the direction of motion and the displacement. Since Roger applies a 100 N force over a distance of 13.0 m, the work done is $100 \, \text{N} \times 13.0 \, \text{m} = 1300 \, \text{J}$.

Question 16

The same constant force is used to accelerate two carts of the same mass,initially at rest,on horizontal frictionless tracks.The force is applied to cart A for twice as long a time as it is applied to cart B.The work the force does on A is W_A;that on B is W_B.Which statement is correct?

Accepted Answer

The answer of The same constant force is used to...

Question 17

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B.Both carts start from rest.The velocities _A and _B of the bodies at the end of distance D are related by

Accepted Answer

The answer of Carts A and B have equal masses...

Question 18

Equal amounts of work are performed on two bodies,A and B,initially at rest,and of masses M and 2M respectively.The relation between their speeds immediately after the work has been done on them is

Accepted Answer

The answer of Equal amounts of work are performed on...

Question 19

If 
= 6)0, 
= 5)0,and α = 40°,determine the scalar product of the two vectors shown.

Accepted Answer

The answer of If 
= 6)0, 
= 5)0,and α =...

Question 20

Two eggs of equal mass are thrown at a blanket with equal velocity.Egg B hits the blanket but egg A hits the wall instead.Compare the work done on the eggs in reducing their velocities to zero.

Accepted Answer

The answer of Two eggs of equal mass are thrown...

Quiz 7: Energy of a System

Negative work can be done

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their speeds at the instant of launch is

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μ_k,then dragged back along the same path to its original position,the work done by friction is

In a contest,two tractors pull two identical blocks of stone the same distance over identical surfaces.However,block A is moving twice as fast as block B when it crosses the finish line.Which statement is correct?

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their kinetic energies at the instant of launch is

When a ball rises vertically to a height h and returns to its original point of projection,the work done by the gravitational force is

A mass attached to the end of a spring is pulled out and released on a surface with friction.The work Done on the mass by the force exerted by the spring

If the scalar (dot) product of two vectors is negative,it means that

A 30-kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s.While she remains seated in the same spot and travels in a circle,the work the seat performs on her in one complete rotation is

Two cannonballs are dropped from a second floor physics lab at height h above the ground.Ball B has four times the mass of ball A.When the balls pass the bottom of a first floor window at height Above the ground,the relation between their kinetic energies,K_A and K_B,is

Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A,and a constant force 2F is applied to B.The relative amounts of work done by the two forces are related by

The work Done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d Is

Two balls,A and B,of mass m and 2m respectively,are carried to height h at constant velocity,but B rises twice as fast as A.The work the gravitational force does on B is

Sally,who weighs 450 N,stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street.He applies a constant 100 N force.

The same constant force is used to accelerate two carts of the same mass,initially at rest,on horizontal frictionless tracks.The force is applied to cart A for twice as long a time as it is applied to cart B.The work the force does on A is W_A;that on B is W_B.Which statement is correct?

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B.Both carts start from rest.The velocities _A and _B of the bodies at the end of distance D are related by

Equal amounts of work are performed on two bodies,A and B,initially at rest,and of masses M and 2M respectively.The relation between their speeds immediately after the work has been done on them is

If = 6) 0, = 5) 0,and α = 40°,determine the scalar product of the two vectors shown.

Two eggs of equal mass are thrown at a blanket with equal velocity.Egg B hits the blanket but egg A hits the wall instead.Compare the work done on the eggs in reducing their velocities to zero.

Quiz 7: Energy of a System

Negative work can be done

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their speeds at the instant of launch is

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μk,then dragged back along the same path to its original position,the work done by friction is

In a contest,two tractors pull two identical blocks of stone the same distance over identical surfaces.However,block A is moving twice as fast as block B when it crosses the finish line.Which statement is correct?

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their kinetic energies at the instant of launch is

When a ball rises vertically to a height h and returns to its original point of projection,the work done by the gravitational force is

A mass attached to the end of a spring is pulled out and released on a surface with friction.The work Done on the mass by the force exerted by the spring

If the scalar (dot) product of two vectors is negative,it means that

A 30-kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s.While she remains seated in the same spot and travels in a circle,the work the seat performs on her in one complete rotation is

Two cannonballs are dropped from a second floor physics lab at height h above the ground.Ball B has four times the mass of ball A.When the balls pass the bottom of a first floor window at height Above the ground,the relation between their kinetic energies,KA and KB,is

Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A,and a constant force 2F is applied to B.The relative amounts of work done by the two forces are related by

The work Done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d Is

Two balls,A and B,of mass m and 2m respectively,are carried to height h at constant velocity,but B rises twice as fast as A.The work the gravitational force does on B is

Sally,who weighs 450 N,stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street.He applies a constant 100 N force.

The same constant force is used to accelerate two carts of the same mass,initially at rest,on horizontal frictionless tracks.The force is applied to cart A for twice as long a time as it is applied to cart B.The work the force does on A is WA;that on B is WB.Which statement is correct?

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B.Both carts start from rest.The velocities A and B of the bodies at the end of distance D are related by

Equal amounts of work are performed on two bodies,A and B,initially at rest,and of masses M and 2M respectively.The relation between their speeds immediately after the work has been done on them is

If = 6) 0, = 5) 0,and α = 40°,determine the scalar product of the two vectors shown.

Two eggs of equal mass are thrown at a blanket with equal velocity.Egg B hits the blanket but egg A hits the wall instead.Compare the work done on the eggs in reducing their velocities to zero.

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μ_k,then dragged back along the same path to its original position,the work done by friction is

Two cannonballs are dropped from a second floor physics lab at height h above the ground.Ball B has four times the mass of ball A.When the balls pass the bottom of a first floor window at height Above the ground,the relation between their kinetic energies,K_A and K_B,is

The same constant force is used to accelerate two carts of the same mass,initially at rest,on horizontal frictionless tracks.The force is applied to cart A for twice as long a time as it is applied to cart B.The work the force does on A is W_A;that on B is W_B.Which statement is correct?

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B.Both carts start from rest.The velocities _A and _B of the bodies at the end of distance D are related by