HW09 - Work and Kinetic Energy
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12/19/22, 12:15 PM
HW09 - Work and Kinetic Energy
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072427
1/22
HW09 - Work and Kinetic Energy
Due: 11:59pm on Monday, November 21, 2022
To understand how points are awarded, read the Grading Policy for this assignment.
When Push Comes to Shove
Two forces, of magnitudes = 100 and = 45.0 , act in opposite directions on a block, which sits atop a frictionless
surface, as shown in the figure. Initially, the center of the block is
at position = -2.00 . At some later time, the block has
moved to the right, and its center is at a new position, = 6.00
.
Part A
Find the work done on the block by the force of magnitude = 100 as the block moves from = -2.00 to
= 6.00 .
Express your answer numerically, in joules.
Hint 1. Formula for the work done by a force
The work done by a force in producing a displacement is given by
,
where is the angle between the two vectors.
ANSWER:
Correct
Part B
Find the work done by the force of magnitude = 45.0 as the block moves from = -2.00 to = 6.00
.
Express your answer numerically, in joules.
= 8.00
12/19/22, 12:15 PM
HW09 - Work and Kinetic Energy
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072427
2/22
Hint 1. Is the work positive or negative?
The force of magnitude acts in the opposite direction to that of the motion of the block. Therefore, the work
done by that force must be negative.
ANSWER:
Correct
Part C
What is the net work done on the block by the two forces?
Express your answer numerically, in joules.
ANSWER:
Correct
Part D
Determine the change
in the kinetic energy of the block as it moves from = -2.00 to = 6.00 .
Express your answer numerically, in joules.
Hint 1. Conservation of energy
The work done on the block goes into changing its kinetic energy. Thus the net work done by the two forces is
equal to the change in the kinetic energy.
ANSWER:
Correct
Problem 9.5 - Enhanced - with Hints and Feedback
A 25 box sliding to the left across a horizontal surface is brought to a halt in a distance of 15 by a horizontal rope
pulling to the right with 15 tension.
Part A
How much work is done by tension?
= -3.60
= 4.40
= 4.40
12/19/22, 12:15 PM
HW09 - Work and Kinetic Energy
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072427
3/22
Express your answer with the appropriate units.
Hint 1. How to approach the problem
Recall the expression for work in terms of force and displacement. To determine the sign, remember that work is
an energy transfer due to mechanical means.
ANSWER:
Correct
Part B
How much work is done by gravity?
Express your answer with the appropriate units.
Hint 1. How to approach the problem
Recall the expression for work in terms of force and displacement. Pay attention to the fact that work also
depends on the angle the force vector makes with the displacement vector.
ANSWER:
Correct
Problem 9.9 - Enhanced - with Hints and Feedback
The cable of a crane is lifting a 950 girder. The girder increases its speed from 0.25 to 1.25 in a distance of
2.3 .
Part A
How much work is done by gravity?
Express your answer with the appropriate units.
Hint 1. How to approach the problem
Recall the expression for work in terms of force and displacement. Remember that its sign depends on the force
and displacement directions.
ANSWER:
= -2.3 = 0
12/19/22, 12:15 PM
HW09 - Work and Kinetic Energy
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072427
4/22
Correct
Part B
How much work is done by tension?
Express your answer with the appropriate units.
Hint 1. How to approach the problem
The tension and gravity do work. Kinetic energy of the system changes. Use the energy principle to find the work
done by tension.
ANSWER:
Correct
The Vector Dot Product
The dot product
is one way of multiplying two vectors.
Part A
shows two vectors and . What is their dot product?
Hint 1. How to approach the problem
=
−2.1×10
4
=
2.2×10
4
12/19/22, 12:15 PM
HW09 - Work and Kinetic Energy
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072427
5/22
The dot product of vectors and is defined as , where and are the magnitudes of
the vectors and is the angle between them.
ANSWER:
Correct
Part B
Vector , and vector . What is their dot product?
Hint 1. How to approach the problem
When written in terms of components and unit vectors, the dot product of vectors and is .
ANSWER:
Correct
Part C
shows two vectors and . What is the angle between
them?
Express your answer in degrees.
Hint 1. How to approach the problem
=
6
=
2
12/19/22, 12:15 PM
HW09 - Work and Kinetic Energy
https://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=10072427
6/22
You could use geometry and trigonometry to find the angle, but it's easier to use the dot product. In Part A you
learned an expression for the dot product involving the angle between the vectors. In Part B you learned how to
use components to calculate the dot product. Combine these to find an expression for , then take the
inverse cosine.
ANSWER:
Correct
Problem 9.18 - Enhanced - with Expanded Hints
The three ropes shown in the bird's-eye view of are used to drag a
crate 3.2 across the floor.
Part A
How much work is done by each of the three forces?
Express your answers in kilojoules separated by commas.
Hint 1. How to approach the problem
Recall the expression for the work performed by a constant force for any specific coordinate system.
You may need to review The Vector Dot Product
.
Hint 2. Simplify: Work done by force What expression should be used to calculate the work of force ? is the distance traveled by the crate.
ANSWER:
= 83
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