Exercise 3.12 H

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

What is the total acceleration at the rim of the wheel at time t = 30.00 s?

Tip: At first, determine the tangential acceleration and the centripetal acceleration. Finally, calculate the vector sum of these.
Answer: $3{,}6\ \frac{m}{s^2}$ and the angle with respect to the radius of the wheel $\theta\approx0{,}4°$

Exercise 3.13 A

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Determine the moment of inertia of the wheel through its center.

Answer: $0{,}078\ kgm^2$

Exercise 3.13 B

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Specify the moment of inertia of the rolling object.

Tip: First derive an expression for the moment of inertia starting from the principle of energy. Then take advantage of the steadily accelerating motion formulas.
Answer: $0{,}000012\ kgm^2$

Exercise 3.13 C

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Specify the moment of inertia of the rolling object.

Tip: First derive an expression for the moment of inertia starting from the principle of energy. Then take advantage of the steadily accelerating motion formulas.
Answer: $0{,}000021\ kgm^2$

Exercise 3.13 D

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Determine the moment of inertia of the wheel through its center.

${\Sigma M=\frac{dL}{dt}}$
Answer: $0{,}073 kgm^2$

Exercise 3.14 A

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Determine the mass of the second wagon (wagon with a spring at the end). How much of kinetic energy is converted into thermal energy in a collision (percentage)?

Answer: 520 g, 57 %

Exercise 3.14 B

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Determine the mass of the second wagon (wagon with a spring at the end). How much of kinetic energy is converted into thermal energy in a collision (percentage)?

Answer: 530 g, 28 %

Exercise 3.14 C

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Determine the mass of the wagon that was not moving at the beginning.

Answer: 550 g

Exercise 3.14 D

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Determine the mass of the second wagon (wagon as shown on the right).

Answer: 580 g

Exercise 3.15 A

DifficultySecondary SchoolHigh school/other
★BasicEasy
★★DemandingBasic
★★★Demanding
★★★★Difficult
★★★★★Very difficult

Determine the modulus of elasticity of the solid metal bar. What metal could the bar be made of? (Note: Video contains audio)

Answer: $192\cdot{10^9}\frac{N}{m^2}$