\( W = Fd\cos\theta \) | \( E_k = \tfrac{1}{2}mv^2 \) | \( E_p = mgh \) | \( E_s = \tfrac{1}{2}kx^2 \) | \( P = W/t \)
\( p = mv \) | \( J = F\Delta t = \Delta p \) | \( g = 9.8 \text{ m/s}^2 \)
Part A: Knowledge & Understanding [15 marks]
1. [3]
A \(75\text{ kg}\) diver jumps from a \(10\text{ m}\) platform. Calculate: a) PE at the top, b) speed entering the water, c) KE at the water surface.
2. [3]
A \(0.145\text{ kg}\) baseball is pitched at \(40\text{ m/s}\) and hit back at \(55\text{ m/s}\). The bat contacts the ball for \(0.002\text{ s}\). Calculate the average force exerted.
3. [3]
A spring (\(k = 400\text{ N/m}\)) launches a \(0.20\text{ kg}\) ball upward from compression of \(0.10\text{ m}\). How high does the ball go?
4. [3]
A \(4.0\text{ kg}\) cart at \(3.0\text{ m/s}\) collides elastically with a \(2.0\text{ kg}\) stationary cart. Find the velocity of each after collision.
5. [3]
Calculate the power output of a \(70\text{ kg}\) person who runs up a \(5.0\text{ m}\) staircase in \(4.0\text{ s}\).
Part B: Thinking [15 marks]
6. [5]
A \(1500\text{ kg}\) car traveling east at \(20\text{ m/s}\) collides with a \(2000\text{ kg}\) truck traveling north at \(15\text{ m/s}\). They lock together. Find the speed and direction of the wreckage.
7. [5]
A pendulum of length \(2.0\text{ m}\) is released from horizontal. At the bottom, it hits and embeds in a \(3.0\text{ kg}\) stationary block. The pendulum bob mass is \(1.0\text{ kg}\). How fast does the combined mass move after impact?
8. [5]
A \(50\text{ kg}\) skier starts from rest at the top of a \(30°\) slope that is \(100\text{ m}\) long. The coefficient of kinetic friction is \(0.10\). Using the work-energy theorem, find the speed at the bottom.
Part C: Communication [15 marks]
9. [5]
Explain why crumple zones, airbags, and seatbelts all reduce injury in car crashes. Use the impulse-momentum theorem (\(J = F\Delta t = \Delta p\)) in your explanation.
0 words
10. [5]
Compare and contrast elastic, inelastic, and perfectly inelastic collisions. For each type: what is conserved, what is not, and give a real-world example.
0 words
11. [5]
A student says: "If I throw a ball upward and catch it at the same height, no work was done because the displacement is zero." Is the student correct? Analyze this claim by considering the work done by different forces (hand, gravity) during the throw and the catch.
0 words
Part D: Application [15 marks]
12. [5]
A bungee jumper (\(80\text{ kg}\)) jumps from a \(50\text{ m}\) bridge. The bungee cord has natural length \(20\text{ m}\) and \(k = 60\text{ N/m}\). How far does the jumper fall before the first rebound? (Hint: set gravitational PE lost = elastic PE gained.)
13. [5]
A hockey puck (\(0.17\text{ kg}\)) sliding at \(25\text{ m/s}\) is stopped by a goalie's glove in \(0.05\text{ s}\). a) Calculate the impulse. b) Calculate the average force. c) If the puck instead bounces off the glove at \(15\text{ m/s}\), is the force greater or less? Show calculations.
14. [5]
A hydroelectric dam converts the PE of falling water into electricity. If \(500\text{ m}^3\) of water per second falls \(80\text{ m}\), and the system is \(85\%\) efficient: a) Calculate the power input (water density = \(1000\text{ kg/m}^3\)). b) Calculate the electrical power output. c) How many homes can this power if each uses \(1.5\text{ kW}\)?