⏱️ Duration: 75 minutes | Total: /60 marks
Show all work including free body diagrams where required. Answers without work receive partial credit at best.
K/U
/15
Thinking
/15
Comm.
/15
Applic.
/15
📋 Formulae Provided
\( v = v_0 + at \) | \( d = v_0 t + \tfrac{1}{2}at^2 \) | \( v^2 = v_0^2 + 2ad \) | \( \Sigma F = ma \)
\( f = \mu N \) | \( F_c = \frac{mv^2}{r} \) | \( a_c = \frac{v^2}{r} \) | \( T = \frac{2\pi r}{v} \) | \( g = 9.8 \text{ m/s}^2 \)
Part A: Knowledge & Understanding [15 marks]
1. [2 marks]
A car accelerates from \( 15 \text{ m/s} \) to \( 35 \text{ m/s} \) in \( 8.0 \text{ s} \). Calculate the acceleration and the distance traveled.
2. [3 marks]
A \( 4.0 \text{ kg} \) block is on a horizontal surface with \( \mu_k = 0.25 \). A horizontal force of \( 20 \text{ N} \) is applied.
a) Draw a complete free body diagram.
b) Calculate the normal force, friction force, and net force.
c) Calculate the acceleration.
3. [2 marks]
State Newton's Third Law and give a specific example from everyday life. Identify the action-reaction force pair in your example.
4. [3 marks]
A ball is thrown horizontally at \( 12 \text{ m/s} \) from a height of \( 20 \text{ m} \).
a) How long does it take to hit the ground?
b) How far does it travel horizontally?
5. [2 marks]
A \( 2.0 \text{ kg} \) object moves in a circle of radius \( 0.80 \text{ m} \) with a period of \( 1.5 \text{ s} \). Calculate the centripetal acceleration.
6. [3 marks]
A \( 6.0 \text{ kg} \) block on a \( 35° \) incline has \( \mu_k = 0.20 \). It is released from rest.
a) Draw a free body diagram with all forces labeled and resolved into components.
b) Calculate the acceleration down the incline.
Part B: Thinking [15 marks]
7. [5 marks]
Two blocks are connected by a string over a frictionless pulley. Block A (\( 8.0 \text{ kg} \)) is on a frictionless table. Block B (\( 5.0 \text{ kg} \)) hangs vertically.
a) Draw free body diagrams for both blocks.
b) Write Newton's 2nd law equations for each block.
c) Solve for the acceleration of the system and the tension in the string.
8. [5 marks]
A car rounds a banked curve (radius \( 120 \text{ m} \), bank angle \( 18° \)). There is no friction.
a) Draw a free body diagram for the car on the banked surface.
b) Show that the speed for no-friction banking is \( v = \sqrt{rg\tan\theta} \).
c) Calculate this speed.
9. [5 marks]
A \( 0.20 \text{ kg} \) ball on a string moves in a vertical circle of radius \( 0.80 \text{ m} \).
a) At the top of the circle, what is the minimum speed to maintain the circular path? (Hint: at minimum speed, \( N = 0 \))
b) If the ball moves at \( 5.0 \text{ m/s} \) at the bottom of the circle, what is the tension in the string?
Part C: Communication [15 marks]
10. [5 marks]
Explain the difference between inertial and non-inertial reference frames. Include:
Definition of each
An example of each
How Newton's laws apply differently in each
The concept of fictitious forces
0 words
11. [5 marks]
A student says: "An object moving in a circle at constant speed has no acceleration because the speed isn't changing." Write a clear response correcting this misconception. Include a diagram.
0 words
12. [5 marks]
Describe, step by step, how to solve a Newton's 2nd Law problem involving an object on an inclined plane with friction. Your guide should be usable by another student. Include: identifying forces, choosing axes, resolving components, and solving.
0 words
Part D: Application [15 marks]
13. [5 marks]
A ski jumper (\( 65 \text{ kg} \)) launches off a ramp at \( 25 \text{ m/s} \) at an angle of \( 35° \) above the horizontal. The landing area is \( 10 \text{ m} \) below the launch point.
a) How long is the jumper in the air?
b) How far (horizontally) does the jumper travel?
14. [5 marks]
An amusement park ride spins riders in a vertical circle of radius \( 8.0 \text{ m} \). The ride completes one revolution every \( 4.0 \text{ s} \). A rider has mass \( 60 \text{ kg} \).
a) What is the rider's speed?
b) What is the normal force on the rider at the top of the loop?
c) What is the normal force at the bottom of the loop?
d) Where does the rider feel heaviest? Lightest? Explain.
15. [5 marks]
A car (\( 1200 \text{ kg} \)) drives over a hill with radius of curvature \( 40 \text{ m} \).
a) At what speed would the car become airborne at the top of the hill? (Hint: this happens when \( N = 0 \))
b) If the car drives at \( 15 \text{ m/s} \), what is the normal force at the top?
c) Explain why road engineers design hills with large radii of curvature.
Evaluation Rubric
Level
Description
%
4
Thorough, insightful, high degree of effectiveness