Quantitative Bar Graphs and Problems

UNIT VII: WS 3b Quantitative Bar Graphs and Problems

General Instructions

• For each situation:

  • Show the system being analyzed in the energy flow diagram.

  • Assume frictionless systems unless stated otherwise.

  • Complete the energy bar graph quantitatively (numerically accurate).

  • Use conservation of energy equations to solve for the required quantity.

Problem 1

• Scenario: A moving cart hits a spring, traveling at $5.0 \frac{m}{s}$ at the time of contact. The cart is motionless at the instant of maximum spring compression.

• Question: By how much is the spring compressed?

• Given:

  • $v = 5.0 \frac{m}{s}$

  • $m = 500 kg$

  • $k = 100 \frac{N}{m}$

  • $\Delta x = 0.30 m$

• Energy Flow Diagram:

  • Initial: $EK$ (Kinetic Energy)

  • Final: $Eel$ (Elastic Potential Energy)

Problem 2

• Scenario: (Building upon Problem 1) Determine the final velocity of the cart, assuming that 10% of the energy is dissipated by friction.

• Energy Flow Diagram:

  • Initial: $EK$ (Kinetic Energy)

  • Final: $EK$ (Kinetic Energy), $Eint$ (Internal Energy)

Problem 3

• Scenario: A block is placed on a spring, compressing it $0.30 m$. The block is then launched by the spring.

• Question: What height does the block reach?

• Given:

  • $\Delta x = 0.30 m$

  • $m = 20 kg$

• Energy Flow Diagram:

  • Initial: $Eel$ (Elastic Potential Energy)

  • Final: $Eg$ (Gravitational Potential Energy)

Problem 4

• Scenario: A bullet strikes a block of wood, which exerts an average force of $50,000 N$ opposing the motion of the bullet.

• Question: How far does the bullet penetrate?

• Given:

  • $F = 50,000 N$

• Energy Flow Diagram:

  • Initial: $EK$ (Kinetic Energy)

  • Final: $Eint$ (Internal Energy)

Problem 5

• Scenario: A $200 kg$ box is pulled at constant speed by an engine a distance of $2.5 m$ across a horizontal surface.

• Given:

  • $m = 200 kg$

  • $d = 2.5 m$

• Tasks:

  • (a) Draw a force diagram of all relevant forces acting on the box.

  • (b) Construct a qualitative energy bar graph/flow diagram for this situation. Specify the system.

  • (c) How much energy is transferred by the engine?

  • (d) What type of motion would occur if the engine pulled with a force of $500 N$? Modify the force diagram and apply Newton's 2nd Law.

• Energy Flow Diagram:

  • Initial: None specified

  • Final: None specified

Problem 6

• Scenario: (Building upon Problem 5) How far could the box in problem 5 be pulled at constant velocity with the expenditure of $8,000 J$ of energy?

• Given:

  • $E = 8,000 J$

Problem 7

• Scenario: A person pulls a $50 kg$ box with a force of $100 N$. The coefficient of kinetic friction is $0.15$.

• Given:

  • $m = 50 kg$

  • $F = 100 N$

  • $\mu_k = 0.15$

• Tasks:

  • (a) Sketch a force diagram for the box.

  • (b) How much of the force acts in the direction of motion? How much energy is transferred (via working) by the person who pulls the box a distance of $10 m$?

  • (c) Is the box moving at constant speed? Explain how you know. What does this tell you about the kinetic energy $E_k$ of the system?

  • (d) How much energy is stored as internal energy due to friction in the pulling process? What eventually happens to this energy?

  • (e) Show that energy is conserved in the system, accounting for all the energy stored and transferred in the process.

• Energy Flow Diagram:

  • Initial: None specified

  • Final: None specified