Free Body Diagram Examples for Impulse-Momentum Problems

📚 Quick Study Guide

• ⚖️ Free Body Diagram (FBD): A visual representation of all forces acting on an object. Isolate the object and draw vectors representing each force.
• импульс Impulse (J): The change in momentum of an object. Mathematically, $J = \int F dt \approx F_{avg} \Delta t$, where $F$ is force and $t$ is time.
• 🚀 Momentum (p): The product of an object's mass and velocity. Expressed as $p = mv$.
• 💥 Impulse-Momentum Theorem: States that the impulse acting on an object is equal to the change in momentum of that object: $J = \Delta p = m(v_f - v_i)$.
• ✍️ System: Clearly define your system. Internal forces within the system do not affect the overall momentum.
• ➕ Vector Addition: Remember that force, impulse, and momentum are vectors! Consider direction when summing forces. Use components if necessary.
• 💡 Problem Solving Steps:
  1. Draw the FBD.
  2. Apply Impulse-Momentum Theorem.
  3. Solve for unknowns.

Practice Quiz

1. Question 1: A 2 kg ball is traveling at 5 m/s to the right. It is then hit with a bat, causing it to move 8 m/s to the left. What is the impulse on the ball?
   1. -6 kg m/s
   2. 6 kg m/s
   3. -26 kg m/s
   4. 26 kg m/s
2. Question 2: A 0.5 kg hockey puck is initially at rest on a frictionless surface. A constant force of 4 N is applied to the puck for 0.1 s. What is the final speed of the puck?
   1. 0.2 m/s
   2. 0.8 m/s
   3. 1.6 m/s
   4. 2.0 m/s
3. Question 3: A 1500 kg car crashes into a wall at 15 m/s. The car comes to a complete stop in 0.15 seconds. What is the average force exerted on the car during the crash?
   1. 150,000 N
   2. -150,000 N
   3. 22,500 N
   4. -22,500 N
4. Question 4: Two ice skaters, with masses of 50 kg and 70 kg, are initially at rest and holding hands. They push off each other. If the 50 kg skater moves at 3 m/s, what is the velocity of the 70 kg skater?
   1. 2.14 m/s (same direction)
   2. 2.14 m/s (opposite direction)
   3. 1.5 m/s (same direction)
   4. 1.5 m/s (opposite direction)
5. Question 5: A tennis ball of mass 0.057 kg is served with a velocity of 50 m/s. If the racket exerts an average force of 200 N on the ball, for how long is the ball in contact with the racket?
   1. 0.0071 s
   2. 0.014 s
   3. 0.14 s
   4. 1.4 s
6. Question 6: A rocket expels exhaust gases at a rate of 5 kg/s with a velocity of 2000 m/s. What is the thrust force on the rocket?
   1. 400 N
   2. 10,000 N
   3. 400,000 N
   4. 1,000 N
7. Question 7: A 0.2 kg baseball is thrown towards a batter at 30 m/s. The batter hits the ball, and it leaves the bat with a velocity of 40 m/s in the opposite direction. What is the magnitude of the impulse on the ball?
   1. 2 Ns
   2. 14 Ns
   3. 7 Ns
   4. 28 Ns