Tutorial Question 1
Main learning points
Main learning points
- Since speed is constant, by Newton's 1st law, there is no net external force acting on the box.
- Opposing frictional force has to be equal in magnitude to horizontal force.
Tutorial Question 2
Main learning points
Main learning points
- Resultant force could be derived from velocity and time duration using Newton's 2nd law, F = ma.
![Picture](/uploads/4/1/0/5/41051203/3331513.png?1425723970)
Tutorial Question 3a
- Direction of drag force due to air resistance is opposite to the direction of the motion.
- Caution: According to Newton's 1st law, there is no "kicking" force after the ball has left the foot.
- The weight and drag force does not necessarily have the same magnitude.
![Picture](/uploads/4/1/0/5/41051203/6695016.png?1425724209)
Tutorial Question 3b
Main learning points
Main learning points
- Drag force is proportional to velocity squared.
- At the peak of the trajectory, since vertical velocity is zero, there is no drag force.
![Picture](/uploads/4/1/0/5/41051203/515488.png?250)
Tutorial Question 4
- The strategy to solve such questions is to derive an equation describing the motion.
- The equation in this scenario could be obtained from a free-body diagram as shown.
- Assuming friction and drag force are negligible, weight is the only external force acting on the skier.
- From the diagram, looking at component of weight parallel to the slope, we use Newton's 2nd law.
W sin θ = ma
mg sin θ = ma
a = g sin θ - (1)
mg sin θ = ma
a = g sin θ - (1)
5. Equation (1) was first seen in PWS2, on the experiment of marble rolling down the inclined plane.
6. Hey! The acceleration down the slope is independent of mass, m
7. Regardless of mass, both skiers will ski down the slope with the same acceleration!
6. Hey! The acceleration down the slope is independent of mass, m
7. Regardless of mass, both skiers will ski down the slope with the same acceleration!
Tutorial Question 5a
Main learning points
Main learning points
- The use of Newton's 2nd law, net external forces = ma, in this case, Weight - Drag Force = ma.
Tutorial Question 5b
Main learning points
Main learning points
- At terminal velocity, acceleration = 0. Newton's 2nd law equation reduces to Newton's 1st law.
For a full walkthrough of question 5. Click here! (ignore the question number in the video)
always use these Steps to solve problems involving Newton's 2nd law
1) Think and Select the system to consider
2) Draw Free body diagram (of 1 system only) include acceleration of the body at the side.
3) take desired direction as positive
4) use equation Fnet = ma,
where fnet refers to the resultant external forces acting on the system.
As simple as 1, 2, 3, 4...
refer to page 9 of notes for more examples.
Tutorial Question 6
(a) At constant velocity, Newton's 1st law is employed, Fnet = 0.
Your role here is to identify the external forces contributing to Fnet.
(b) As the elevator is decelerating, Newton's 2nd law is invoked, Fnet = ma.
- Try looking at the elevator example in lecture notes.
- Draw 3 separate FBDs of the woman, scale and the elevator. (this has been done in lecture, try them on your own to test your mastery of this classic question.)
- You should be able to relate the forces acting on different systems and see how each change in one of the forces affect the rest.
(a) At constant velocity, Newton's 1st law is employed, Fnet = 0.
Your role here is to identify the external forces contributing to Fnet.
(b) As the elevator is decelerating, Newton's 2nd law is invoked, Fnet = ma.
Tutorial Question 7
(a) Thought process:
(b) Thought process:
(c) Thought process:
For a full walkthrough of question 7. Click here! (ignore the question number in the video)
(a) Thought process:
- I could determine acceleration, a, quickly by using Newton's 2nd law.
- I need to find the length s, required.
- An equation the relates s and a, without time as a variable would be v2 = u2+ 2as. (consider using SUVAT table if you have difficulty identifying the correct equation here)
- I could now substitute in the values provided, as well as the acceleration a, I calculated, to obtain s.
(b) Thought process:
- The steps here are the same as in part (a). The differences here are merely the total mass and the final velocity v.
(c) Thought process:
- What factors are present in real life that I did not consider in my equations in (a) and (b)?
For a full walkthrough of question 7. Click here! (ignore the question number in the video)
Tutorial Question 8
Thought process:
For a full walkthrough of question 8. Click here! (ignore the question number in the video)
Thought process:
- I am provided with final and initial speeds and distance. How can I relate them to the frictional force?
- Force could be related to speeds and distance via acceleration (F=ma)!
- The kinematics equation that relates velocities, distance and acceleration without time could be figure out easily (SUVAT table).
- Execute this strategy and the problem is solved!
For a full walkthrough of question 8. Click here! (ignore the question number in the video)
Tutorial Question 9
Thought process:
For a full walkthrough of question 9. Click here! (ignore the question number in the video)
Thought process:
- I have to find the speed but I am given Force. What equation relates them?
- As per question 8, I can relate the Force to speed using (F=ma) and a kinematics equation.
- Otherwise, I could also employ concepts from impulse. The change in momentum = area under F-t graph.
For a full walkthrough of question 9. Click here! (ignore the question number in the video)
Tutorial Question 10
Thought process:
For a full walkthrough of question 10. Click here! (ignore the question number in the video)
Thought process:
- Question demands me to find the driving Force. This force has its direction going upwards and parallel to the slope.
- There are many other external forces acting on the car; weight, total resistive force and normal reaction force.
- I merely need to resolve all other external forces into the plane parallel to the slope.
- Taking forward direction of the car to be positive, I use Newton's 2nd law to solve for the unknown driving Force.
For a full walkthrough of question 10. Click here! (ignore the question number in the video)
Tutorial Question 11
Hints:
(a)
The law of inertia (Newton's 1st law) is invoked here. As the train carrying the bob accelerates, the pendulum bob resists change to its motion.
(b)
The bob is accelerating with the train. Which force provides for this acceleration? (which component of the force?)
Draw FBD and you can figure it out.
(c)
This requires merely basic use of Newton's 2nd law.
(d)
Identify the angle of tilt on your FBD. Employ simple trigo ratios to determine the angle.
Challenge!!! How would the FBD differ if you were in the train carriage and oblivious to the environment outside the carriage? (not knowing that the train is accelerating)
For a full walkthrough of question 11. Click here! (ignore the question number in the video)
Hints:
(a)
The law of inertia (Newton's 1st law) is invoked here. As the train carrying the bob accelerates, the pendulum bob resists change to its motion.
(b)
The bob is accelerating with the train. Which force provides for this acceleration? (which component of the force?)
Draw FBD and you can figure it out.
(c)
This requires merely basic use of Newton's 2nd law.
(d)
Identify the angle of tilt on your FBD. Employ simple trigo ratios to determine the angle.
Challenge!!! How would the FBD differ if you were in the train carriage and oblivious to the environment outside the carriage? (not knowing that the train is accelerating)
For a full walkthrough of question 11. Click here! (ignore the question number in the video)
Tutorial Question 12
Hints:
(a)
Understand that with Newton's 3rd law, the tension on P is the same as the tension on Q.
(b)
(c)
For a full walkthrough of question 12. Click here! (ignore the question number in the video)
Hints:
(a)
- For this question, draw the FBD of the entire system to determine the acceleration of the entire system of 2 blocks. (they have the same acceleration)
- To solve for forces acting on individual systems, draw the FBD of each block separately. (you actually only need to consider block P)
- Use Newton's 2nd law with steps delineated above (before tutorial Qn 6).
Understand that with Newton's 3rd law, the tension on P is the same as the tension on Q.
(b)
- Refer to step 1 in part (a).
- Use Newton's 2nd law with steps delineated above.
(c)
- The easy way is to consider block P alone.
For a full walkthrough of question 12. Click here! (ignore the question number in the video)
Tutorial Question 13
Thought process:
(a)
(b)
(c)
For a full walkthrough of question 13. Click here! (ignore the question number in the video)
Thought process:
(a)
- In order to determine the acceleration of the train, I should consider the entire train as a system.
- In this way, the net external forces will mainly be the thrust - frictional forces.
- I am considering all horizontal forces, does the weight of the train given in the question matter?
(b)
- Since the tension only affects two cars, I have to now consider one car as a system.
- I know that by Newton's 3rd law, the tension on the first car = tension on the second car (for the tension in the coupling between them)
- Considering the first car as a system, the net external force on it is given by its thrust - tension - frictional force.
- By Newton's 2nd law, the net external force = ma, where a is the acceleration determined in (a).
(c)
- Which car should I consider as a system? Both are possible, yet, considering the last car will be easier since there are less external forces acting on it.
- I can now follow the steps done in (b) to obtain the solution.
For a full walkthrough of question 13. Click here! (ignore the question number in the video)
Tutorial Question 14
Thought process:
(a)
(b)
For a full walkthrough of question 14. Click here!
Thought process:
(a)
- I must first choose the system to apply Newton's second law. I can take all 3 blocks as an entire system, or consider each block as a system individually. Which should I do?
- I will remember to take sign conventions.
- I can now draw FBDs on the system(s).
- Ensure that all EXTERNAL forces are drawn on the system.
- Apply Newton's 2nd law, keeping in mind the sign conventions on the forces and acceleration vectors.
- Look at the number of unknowns and construct the same number of equations using step 5 above. Solve these unknowns by using simultaneous equations.
(b)
- Employ SUVAT table as in kinematics.
- Solve as I have practiced many times before by choosing the proper equation to use.
For a full walkthrough of question 14. Click here!
Tutorial Question 15
Thought process:
(a)
For a full walkthrough of question 15. Click here!
Thought process:
(a)
- I must first choose the system to apply Newton's second law. I can take all 2 blocks as an entire system, or consider each block as a system individually. Which should I do?
- I will remember to take sign conventions.
- I can now draw FBDs on the system(s).
- Ensure that all EXTERNAL forces are drawn on the system. (may be the greatest challenge for this question.)
- Apply Newton's 2nd law, keeping in mind the sign conventions on the forces and acceleration vectors.
- Look at the number of unknowns and construct the same number of equations using step 5 above. Solve these unknowns by using simultaneous equations.
- Solving for acceleration in part (a), I only need to substitute the value into the equation constructed in part (a) where there is an unknown tension and solve for it.
For a full walkthrough of question 15. Click here!
Tutorial Question 16
Thought process:
This question seems familiar. Have I seen something familiar somewhere before? (provided that I am paying attention during lessons of course!)
For a full walkthrough of question 16. Click here!
Thought process:
This question seems familiar. Have I seen something familiar somewhere before? (provided that I am paying attention during lessons of course!)
For a full walkthrough of question 16. Click here!
Tutorial Question 17
Learning Outcomes:
(a)
(b)
Learning Outcomes:
(a)
- Apply equation Δp = (Fnet )(Δt), where Fnet is the average force here.
(b)
- Understand that Δp = pfinal- pinitial .
Tutorial Question 18
Learning Outcomes:
(a)
(b)
Discerning students should identify in their heads, whether this collision is elastic or inelastic.
For a full walkthrough of question 18. Click here!
Learning Outcomes:
(a)
- Draw diagrams and fill in details to illustrate question.
- Apply Principle of Conservation of Momentum, where initial momentum = final momentum.
(b)
- Calculate the difference between initial and final kinetic energy.
Discerning students should identify in their heads, whether this collision is elastic or inelastic.
For a full walkthrough of question 18. Click here!
Tutorial Question 19
Learning Outcomes:
(b)
(c)
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Learning Outcomes:
(b)
- The change in momentum in time period, t = the area under the Force - Time graph in the time period, t.
(c)
- Apply area of triangle and concept employed in part (b).
For a full walkthrough of question 19. Click here!
Tutorial Question 20
Skills required:
(a), (b)
For a full walkthrough of question 20. Click here!
Skills required:
(a), (b)
- Drawing/visualising initial and final systems with all information from the question.
- Apply principle of conservation of momentum create equation of diagram. Solve equation.
For a full walkthrough of question 20. Click here!
Tutorial Question 21
Skills required:
(a)
For a full walkthrough of question 21a. Click here!
(b)
For a full walkthrough of question 21b. Click here!
Skills required:
(a)
- Drawing/visualising initial and final systems with all information from the question.
- Apply principle of conservation of momentum create equation of diagram. Solve equation.
For a full walkthrough of question 21a. Click here!
(b)
- Understand that shortest time means that man has to fire whenever he can to achieve maximum speed.
- Identifying pattern from equation. Realising that every time the bullet is shot in one direction, man increases speed by same magnitude in opposite direction.
- Understand that for different time intervals, man has different speeds. Therefore, displacement for each time interval needs to be calculated separately.
- Solving for unknown t remaining, using equation Δt = Δs/Δv.
For a full walkthrough of question 21b. Click here!