ā±ļø Duration: 75 minutes | Total: /60 marks. Show all work; draw FBDs where required. Use \( g = 9.8 \) m/sĀ².
K/U
/15
Thinking
/15
Comm.
/15
Applic.
/15
Formulae: \( \Sigma F = ma \), \( F_g = mg \), \( f_k=\mu_k N \), \( f_s\le\mu_s N \), \( F_\parallel=mg\sin\theta \), \( N=mg\cos\theta \), \( g=9.8 \) m/sĀ²
Part A ā Knowledge & Understanding [15 marks]
1. [3 marks]
State Newton's three laws of motion. For each law, give a concrete example.
2. [3 marks]
A \(4.0\)-kg block is on a horizontal surface with \( \mu_k = 0.30 \). A horizontal force of \(20\) N is applied. (a) Draw the FBD. (b) Calculate normal force, friction, net force, and acceleration.
[FBD]
3. [2 marks]
MC: A \(10\)-kg object falls in air at terminal velocity. The net force on the object is:
4. [4 marks]
A child pulls a sled with mass \(8.0\) kg using a rope at \(25Ā°\) above horizontal with a force of \(40\) N. There is no friction. (a) Draw the FBD. (b) Calculate the horizontal acceleration. (c) Calculate the normal force.
5. [3 marks]
State Newton's third law in your own words. Identify the action-reaction pair when you walk forward on the sidewalk. Why does the Earth not visibly accelerate backward?
Part B ā Thinking & Investigation [15 marks]
6. [5 marks]
A \(12\)-kg crate sits on a ramp inclined at \(28Ā°\). The coefficient of static friction is \(\mu_s = 0.45\) and kinetic is \(\mu_k = 0.30\). (a) Will the crate slide? Justify with calculations. (b) If a person gives it a small push to start, calculate the acceleration once it slides.
7. [5 marks]
An Atwood machine has masses \(m_1 = 4.0\) kg and \(m_2 = 6.0\) kg connected over a frictionless, massless pulley. (a) Derive the formula for acceleration of the system. (b) Calculate \(a\) and the tension \(T\) in the rope.
8. [5 marks]
Investigation design: Describe an experiment to determine the coefficient of kinetic friction between a wood block and a wooden plank. Identify variables (IV/DV/CV), required equipment, key measurements, calculation, and a major source of error with a way to reduce it.
Part C ā Communication [15 marks]
9. [5 marks]
Draw a clearly labelled FBD for each: (i) a car accelerating forward; (ii) a skydiver at terminal velocity; (iii) a block sliding up a frictionless incline. Use arrows scaled to relative magnitudes.
[FBDs i, ii, iii]
10. [5 marks]
In one paragraph (4ā6 sentences), explain ā using Newton's second law ā why a car with anti-lock brakes (ABS) stops in a shorter distance than one with locked wheels. Use correct vocabulary (static vs. kinetic friction, \(\mu_s > \mu_k\)).
11. [5 marks]
Compare and contrast (table OR paragraph form): static friction vs. kinetic friction. Include: when each acts, formulas, magnitude relationship, dependence on speed, and one real-world example.
Part D ā Application [15 marks]
12. [5 marks]
STSE ā Vehicle safety: A \(1500\)-kg car travelling at \(20\) m/s comes to rest in \(2.0\) s during a crash. (a) Calculate the deceleration. (b) Calculate the average force on the car. (c) Repeat (b) if a crumple zone increases stopping time to \(0.20\) s vs. \(0.020\) s for a rigid car. (d) Explain in 2ā3 sentences how crumple zones, seat belts, and airbags work together to protect occupants.
13. [5 marks]
A \(50\)-kg skier slides down a \(15Ā°\) slope with \( \mu_k = 0.05 \). (a) Calculate the acceleration. (b) Starting from rest, calculate the speed after \(60\) m. (c) If the skier suddenly enters a flat snowy patch (\( \mu_k = 0.05 \)), how far does she travel before stopping?
14. [5 marks]
A \(2.0\)-kg block (A) sits on top of a \(6.0\)-kg block (B). B is pushed across a frictionless floor by a horizontal force of \(40\) N applied to B. The coefficient of static friction between A and B is \(\mu_s = 0.30\). (a) Calculate the acceleration of the system. (b) Calculate the friction force on A from B that accelerates A. (c) Will A slide on B? Justify.