Physics 211
Homework Problems Unit 5: One-Dimensional Forces, Mass, and Motion
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Unit 5 Homework Problems To get credit for the homework problems, you must include all of the following: 1. 2. 3. 4.
All equations must be solved in symbol form before substituting in any numbers. All numbers substituted into the equations must have the correct units and number of significant figures, and the correct vector notation (where appropriate). All final numerical answers must have the correct units, correct number of significant figures, and correct vector notation (where appropriate), All problems should include a reference to the Activity Guide activity or activities that are related to the problem, a discussion of how the activity is related, and a discussion of the concepts that were learned in the activity. UNIT 5 HOMEWORK AFTER SESSION ONE
5-1)
Zach pulls Kenzie across a smooth floor with a big spring scale that is stretched to a constant length. In one case she is riding on a low friction cart and in the other case she is sliding along the floor while sitting in a plastic bag. A motion detector is set up to track her motion in each time. The position-time graphs of her motion are shown below.
(a)
Which graph depicts motion at a constant velocity? Pull Project 1 (on the right) or Pull Project 2 (on the left)? Explain.
(b)
Which graph depicts motion at a roughly constant acceleration? Explain.
(c)
Which graph demonstrates that something pulled with a constant force moves with a constant velocity? Explain.
(d)
Which graph demonstrates that something pulled with a constant force moves with a constant acceleration? Explain.
(e)
Which graph is most likely to show Kenzie’s motion when she is rolling on the cart? Please justify your answer in terms of what you observed in class.
(f)
Can you explain why it is possible to get two different types of motion even though Kenzie is being pulled with a constant force in both cases?
Physics 211
Homework Problems Unit 5: One-Dimensional Forces, Mass, and Motion
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5-2)
The graph and data table that follow below shows data recorded by a motion detector for Kenzie’s position vs. time as she is being pulled across the floor with a steady force while riding on a low friction cart.
(a)
Since the graph looks parabolic (that is, like a 2nd order polynomial), find a kinematic equation that describes the data in the first 3 seconds of Kenzie’s motion (for the first 7 data points). To do this, transfer the data to an Excel Modeling Worksheet spreadsheet and model the data. I want you to continue practicing your modeling skills, so please do not use the “Add Trendline” feature of Excel. Write down the equation you found in the form x = c0 + c1t + c2t 2 . In other words, determine the best fit estimates for the values of c0 , c1 , and c2 . (Don’t forget your units!)
t (s) 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00
x (m) 1.05 1.20 1.44 1.59 1.99 2.52 3.15 3.88 4.66
(b)
According to the equation you obtained, what is Kenzie’s initial position relative to the motion detector (at t = 0.0 s )? What is her initial velocity (at t = 0.0 s )? What is the value of the acceleration between t = 0.0 s and t = 3.0 s? Hint: The acceleration is not c2 .
(c)
According to the equation, when is the acceleration positive, negative, or zero during the time period between 0.00 s and 3.00 s? Is the acceleration constant during that entire period of time? What is the evidence for this?
(d)
Use the kinematic equation you found to predict the x-value of Kenzie’s position at t =4.00 s. Recall that this is a special case where t1 = 0 s , so that ( t − t1 ) = t .
(e)
How does your predicted position compare with the measured position? Please list both positions as part of your answer. (You may also need to do a % difference.)
Physics 211
Homework Problems Unit 5: One-Dimensional Forces, Mass, and Motion
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UNIT 5 HOMEWORK AFTER SESSION TWO 5-3)
(a) A force is applied to an object that experiences very little friction. This force causes the object to move resulting in the acceleration vs. time graph as shown below. Draw a set of graph axes with the same number of time units as that shown in the acceleration graph and carefully sketch the shape of a possible graph of force vs. time on the object.
a (m/s2)
+
0
–
(b)
0
1
2
t (s)
3
4
5
A force is applied to an object that experiences very little friction. This force causes the object to move resulting in the velocity vs. time graph shown below. Draw a set of graph axes with the same number of time units as that shown in the velocity graph and carefully sketch the shape of a possible graph of acceleration vs. time for the object.
v (m/s)
+
0
– 0.0
1.0
2.0 t (s)
3.0
4.0
(c)
Refer to the velocity vs. time graph shown in part (b) or the acceleration vs. time graph you sketched. Draw a set of graph axes with the same number of time units as that shown in the velocity graph and carefully sketch the shape of a possible graph of force vs. time for the object.
5-4)
In the following situations friction is small and can be ignored. Consider whether the net or combined force on a small cart needs to be positive, negative or zero to create the following motions. Sketch graphs that show the shapes of the velocity and force functions in each case. Use the format shown in the graphs below. (Draw a separate set of Velocity vs. Time & Force vs. Time graphs for each part (a) through (d).)
Physics 211
Homework Problems Unit 5: One-Dimensional Forces, Mass, and Motion
+ Force (N)
Velocity (m/s)
+
0
–
0
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2
4
Time (seconds)
6
0
–
0
2
4
Time (seconds)
6
(a)
The cart is moving in the positive direction away from the origin at a constant velocity.
(b)
The cart moves in the negative direction toward the origin speeding up at a steady rate until it reaches a constant velocity after 3 seconds.
(c)
The cart moves in the negative direction toward the origin slowing down at a steady rate, turns around after 2 seconds and then moves away from the origin speeding up at the same steady rate.
(d)
The cart moves in the positive direction away from the origin and slows down for 3 seconds and then speeds up for 3 seconds.
5-5)
The spring scale in the diagram below reads 10.5 N. The cart moves toward the right with an acceleration toward the right of 3.5 m/s2
(a)
Suppose a second spring scale is combined with the first and acts in the same direction as shown in the diagram that follows. The spring scale FA still reads 10.5 N.
The cart now moves toward the right with an acceleration toward the right of 4.50 m/s2. What is the net force on the cart? What does spring scale FB read? Show your calculations and explain. (b)
Suppose a second spring scale is combined with the first and acts in the opposite direction as shown in the diagram that follows. The spring scale FA still reads 10.5 N.
The cart now moves toward the right with an acceleration toward the right of 2.50 m/s2. What is the net force on the cart? What does spring scale FB read? Show your calculations and explain. (c)
Which of Newton’s first two laws apply to the situations in this problem?
Physics 211
Homework Problems Unit 5: One-Dimensional Forces, Mass, and Motion
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5-6)
Two forces are applied to a cart with two different spring scales as shown below. The spring scale FA reads 15 N.
(a)
The cart had an initial velocity of 0.00 m/s when the two forces were applied. It remains at rest after the combined forces are applied. What is the net force on the cart? What does spring scale FB read? Show your calculations and explain.
(b)
The cart had an initial velocity of + 0.75 m/s and so it was moving to the right when the two forces were applied. It continues moving to the right at that same velocity after the combined forces are applied. What is the net force on the cart? What does spring scale FB read? Show your calculations and explain.
(c)
The cart had an initial velocity of – 0.39 m/s and so it was moving to the left when the two forces were applied. It continues moving to the left at that same velocity after the combined forces are applied. What is the net force on the cart? What does spring scale FB read? Show your calculations and explain.
(d)
Which of Newton’s first two laws apply to the situations in this problem? UNIT 5 HOMEWORK AFTER SESSION THREE
5-7)
Suppose you have the following equipment available: an electronic balance as well as a motion detector and an electronic force sensor attached to a computer-based laboratory system. You would like to determine the mass of a block of ice that can slither smoothly along a very level table top without noticeable friction.
(a)
Describe how you would use some of the equipment to find the gravitational mass of the ice.
(b)
Describe how you would use some of the equipment to find the inertial mass of the ice.
(c)
Based on the activities you completed in Section 5.9 in Unit 5, do you predict that the values for your two types of mass will be the same or different?
5-8)
(a) Suppose a toy car moves along a horizontal line without friction and a constant force is applied to the car toward the right.
Sketch a set of axes like those shown below and then use a solid line to sketch the shape of the acceleration-time graph of the car.
Homework Problems Unit 5: One-Dimensional Forces, Mass, and Motion
Acceleration (m/s2)
Physics 211
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+ 0 –
0
Time (seconds)
(b)
Two more identical cars are piled/glued on top of the first car and the same constant force is applied to the three cars. Use a dashed line to sketch the acceleration-time graph of the “triplecar”. Explain any differences in this graph compared to the acceleration-time graph of the car with the original mass.
5-9)
For this problem, you are seeing if using only 2 batteries in the fan cart will give a large enough thrust force. In other words, can we ignore the friction force from the cart wheel-bearings because it is small compared to the thrust force from the fan (actually, the air)? To do this, you will collect motion data for the fan cart on the top track in the movie pasco005.mov. I’ve created a pasco005.cmbl file that is on the homework page. Save both the pasco005.mov file and the pasco005.cmbl file to the Westminster Anywhere desktop, and then double click on the pasco005.cmbl file to open Logger Pro. The pasco005.mov will automatically open in Logger Pro, and the movie will already be scaled and the coordinate system origin placed in the correct location.
(a)
Examine the pasco005.mov movie casually by playing it. Is the fan cart accelerating? If so, is the acceleration positive or negative. Collect horizontal position data for the cart for the full 3.0 s of the movie. Transfer your time and position data to a ModelingWorksheet.xlsx spreadsheet.
(b)
Find the acceleration of the fan cart for when it is slowing down. To do this, model the horizontal position data, trying to get the model to match the position data from 0.0 s to 1.4 s as best as possible. (Remember, the first kinematic equation is x = x1 + v1 ( t − t1 ) + 12 a ( t − t1 ) , where t1 = 0s 2
for this case. Be sure to copy your model equation down for the full 3.0 s). Is the acceleration of the fan cart constant while it is slowing down? Does your model match the position data for while the fan cart is speeding up very well? Is the acceleration constant for the full 3.0 s? (c)
Find the acceleration of the fan cart for when it is speeding up. To do this, model the horizontal position data, trying to get the model to match the position data from 1.5 s to 3.0 s as best as possible. (For this case, t1 = 1.5s in your model). Is the acceleration of the cart constant while it is speeding up? Is the acceleration of the fan cart while it is speeding up larger, smaller, or the same as the acceleration of the fan cart while it is slowing down?
(d)
Using your results from parts (b) and (c), find the magnitude of the thrust force from the fan, and the magnitude of the friction force from the wheel-bearings. By what factor is the thrust force larger than the friction force? Is this large enough to ignore the friction force from the wheelbearings. Hint: Apply Newton’s 2nd Law twice, once for the fan cart slowing down and once for the fan cart speeding up, and assume that the magnitude of the thrust force from the fan and the magnitude of the friction force from the wheel-bearings are both constant for the full 3.0 s.
