Question 1

For the vectors shown in the figure, assume numbers are accurate to two significant figures. The scalar product  × 
Is closest to

Accepted Answer

The answer of For the vectors shown in the figure,...

Question 2

The scalar product of vector  = 3.00 
+ 2.00 
And vector 
Is 10.0. Which of the following vectors could be vector 
?

Accepted Answer

The answer of The scalar product of vector  =...

Question 3

A crane lifts a 425 kg steel beam vertically a distance of 117 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

Accepted Answer

The work done by the crane is calculated using the formula: Work = Force × Distance. The force exerted by the crane is the sum of the gravitational force (mg) and the additional force due to acceleration (ma). Therefore, Force = m(g + a) = 425 kg × (9.8 m/s² + 1.8 m/s²) = 425 kg × 11.6 m/s² = 4930 N. The work done is then 4930 N × 117 m = 5.8 × 10⁵ J.

Question 4

Three forces, F₁ = 20.0 N, F₂ = 40.0 N, and F₃ = 10.0 N act on an object with a mass of 2.00 kg which can move along a frictionless inclined plane as shown in the figure. The questions refer to the instant when the object has moved through a distance of 0.600 m along the surface of the inclined plane in the upward direction. Calculate the amount of work done by (a) F₁ (b) F₂ (c) F₃.

Accepted Answer

The answer of Three forces, F₁ = 20.0 N, F₂...

Question 5

Determine the scalar product of  = 6.0 
+ 4.0 
- 2.0 
And 
= 5.0 
- 6.0 
- 3.0 
.

Accepted Answer

The answer of Determine the scalar product of  =...

Question 6

Find the net work done by friction on the body of a snake slithering in a complete circle of 3.93 m radius. The coefficient of friction between the ground and the snake is 0.25, and the snake's weight is

Accepted Answer

The answer of Find the net work done by friction...

Question 7

The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

Accepted Answer

The answer of The plot in the figure shows the...

Question 8

If  
= 3  
-  
+ 4  
and  
= x  
+  
- 5  
, find x so  
will be perpendicular to  
.

Accepted Answer

The answer of If  
= 3  
- ...

Question 9

Two boys searching for buried treasure are standing underneath the same tree. One boy walks 18 m east and then 18 m north. The other boy walks 16 m west and then 11 m north. Find the scalar product of their net displacements from the tree.

Accepted Answer

The answer of Two boys searching for buried treasure are...

Question 10

The angle between vector  = 2.00 
+ 3.00 
And vector 
Is 45.0°. The scalar product of vectors 
And 
Is 3.00. If the x component of vector 
Is positive, what is vector 
.

Accepted Answer

The answer of The angle between vector  = 2.00...

Question 11

What is the angle between the vector  = +3 
- 2 
- 3 
And the +y-axis?

Accepted Answer

The answer of What is the angle between the vector...

Question 12

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?

Accepted Answer

The answer of A traveler pulls on a suitcase strap...

Question 13

A rectangular box is positioned with its vertices at the following points:
A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3)
B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3)
If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to:

Accepted Answer

The answer of A rectangular box is positioned with its...

Question 14

A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do?

Accepted Answer

The answer of A student slides her 80.0-kg desk across...

Question 15

An object is acted upon by a force that represented by the force vs. position graph in the figure. What is the work done as the object moves
(a) from 4 m to 6 m?
(b) from 6 m to 12 m?

Accepted Answer

The answer of An object is acted upon by a...

Question 16

Determine the angle between the directions of vector  = 3.00 
+ 1.00 
And vector 
= -3.00 
+ 3.00 
.

Accepted Answer

The answer of Determine the angle between the directions of...

Question 17

A potential energy function for system 1 is given by U₁(x) = Cx² + Bx³. The potential energy function for system 2 is given by U₂(x) = A + Cx² + Bx³, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?

Accepted Answer

The force on a system is the negative gradient of the potential energy function with respect to position. Since both potential energy functions have the same terms (except for the added constant A in system 2), the force on the two systems will be identical at a given position. Therefore, choice B is correct.

Question 18

Which, if any, of the following statements concerning the work done by a conservative force is NOT true?

Accepted Answer

All the statements provided are true characteristics of a conservative force. Conservative forces, such as gravity or spring forces, have the property that the work done is independent of the path taken, depends only on the initial and final positions, and is zero if the starting and ending points are the same.

Question 19

An airplane flies 120 km at a constant altitude in a direction 30.0° north of east. A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west. How much work is done on the plane by the air?

Accepted Answer

The work done by the air on the plane is given by the dot product of the force vector and the displacement vector:

$W = \vec{F} \cdot \Delta \vec{r}$

We can split the force vector into its horizontal and vertical components, since the displacement vector is also split into those components (as they are perpendicular):

$\vec{F} = F_x \hat{i} + F_y \hat{j}$

$\Delta \vec{r} = \Delta x \hat{i} + \Delta y \hat{j}$

\begin{align*}
W &= (F_x \hat{i} + F_y \hat{j}) \cdot (\Delta x \hat{i} + \Delta y \hat{j}) \
&= F_x \Delta x + F_y \Delta y \
&= (2.40 	ext{ kN})(-120 	ext{ km}\sin 10^\circ) + (2.40 	ext{ kN})(120 	ext{ km}\cos 10^\circ) \
&= -2.71 	imes 10^{10} 	ext{ J}
\end{align*}

Note that the negative sign means that the work done by the air on the plane is negative, indicating that the plane lost energy to the air.

Question 20

You carry a 7.0 kg bag of groceries 1.2 m above the level floor at a constant velocity of 75 cm/s across a room that is 2.3 m room. How much work do you do on the bag in the process?

Accepted Answer

When carrying an object at a constant velocity, the net force acting on the object is zero, therefore no work is done on the object. Work is only done when a force causes a displacement along the direction of the force, and in this case there is no such force.

Quiz 11: Work

For the vectors shown in the figure, assume numbers are accurate to two significant figures. The scalar product × Is closest to

The scalar product of vector = 3.00 + 2.00 And vector Is 10.0. Which of the following vectors could be vector ?

A crane lifts a 425 kg steel beam vertically a distance of 117 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s2? Neglect frictional forces.

Determine the scalar product of = 6.0 + 4.0 - 2.0 And = 5.0 - 6.0 - 3.0 .

Find the net work done by friction on the body of a snake slithering in a complete circle of 3.93 m radius. The coefficient of friction between the ground and the snake is 0.25, and the snake's weight is

The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

If = 3 - + 4 and = x + - 5 , find x so will be perpendicular to .

Two boys searching for buried treasure are standing underneath the same tree. One boy walks 18 m east and then 18 m north. The other boy walks 16 m west and then 11 m north. Find the scalar product of their net displacements from the tree.

The angle between vector = 2.00 + 3.00 And vector Is 45.0°. The scalar product of vectors And Is 3.00. If the x component of vector Is positive, what is vector .

What is the angle between the vector = +3 - 2 - 3 And the +y-axis?

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?

A rectangular box is positioned with its vertices at the following points: A = (0,0,0) C = (2,4,0) E = (0,0,3) G = (2,4,3) B = (2,0,0) D = (0,4,0) F = (2,0,3) H = (0,4,3) If the coordinates all have three significant figures, the angle between the line segments AG and AH is closest to:

A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do?

An object is acted upon by a force that represented by the force vs. position graph in the figure. What is the work done as the object moves (a) from 4 m to 6 m? (b) from 6 m to 12 m?

Determine the angle between the directions of vector = 3.00 + 1.00 And vector = -3.00 + 3.00 .

A potential energy function for system 1 is given by U1(x) = Cx2 + Bx3. The potential energy function for system 2 is given by U2(x) = A + Cx2 + Bx3, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?

Which, if any, of the following statements concerning the work done by a conservative force is NOT true?

An airplane flies 120 km at a constant altitude in a direction 30.0° north of east. A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west. How much work is done on the plane by the air?

You carry a 7.0 kg bag of groceries 1.2 m above the level floor at a constant velocity of 75 cm/s across a room that is 2.3 m room. How much work do you do on the bag in the process?

A crane lifts a 425 kg steel beam vertically a distance of 117 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s²? Neglect frictional forces.

A potential energy function for system 1 is given by U₁(x) = Cx² + Bx³. The potential energy function for system 2 is given by U₂(x) = A + Cx² + Bx³, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position?