Questions: Un carro de montaña rusa de masa m=580 kg, pasa por el punto A de la figura con rapidez vA=4,0 m/s, luego desciende por el riel hasta que enfrenta un loop donde realiza una vuelta en 360° con radio de curvatura R=4,0 m. La base del loop se encuentra a una altura h=2,0 m sobre el suelo. Considere despreciable el roce entre el riel y el carro. Si el punto A se encuentra a la altura H=12 m de la pregunta anterior ¿Con qué rapidez llega el carro al piso, al finalizar su recorrido? (A) vf=14,3 m/s (B) vf=15,3 m/s (C) vf=14,8 m/s (D) vf=15.8 m/s (E) vj=11,3 m/s

Un carro de montaña rusa de masa m=580 kg, pasa por el punto A de la figura con rapidez vA=4,0 m/s, luego desciende por el riel hasta que enfrenta un loop donde realiza una vuelta en 360° con radio de curvatura R=4,0 m. La base del loop se encuentra a una altura h=2,0 m sobre el suelo. Considere despreciable el roce entre el riel y el carro. Si el punto A se encuentra a la altura H=12 m de la pregunta anterior ¿Con qué rapidez llega el carro al piso, al finalizar su recorrido? (A) vf=14,3 m/s (B) vf=15,3 m/s (C) vf=14,8 m/s (D) vf=15.8 m/s (E) vj=11,3 m/s
Transcript text: Un carro de montaña rusa de masa $m=580 \mathrm{~kg}$, pasa por el punto $A$ de la figura con rapidez $v_{A}=4,0 \frac{\mathrm{m}}{\mathrm{s}}$, luego desciende por el riel hasta que enfrenta un loop donde realiza una vuelta en $360^{\circ}$ con radio de curvatura $R=4,0 \mathrm{~m}$. La base del loop se encuentra a una altura $\mathrm{h}=2,0 \mathrm{~m}$ sobre el suelo. Considere despreciable el roce entre el riel y el carro. Si el punto $A$ se encuentra a la altura $H=12 \mathrm{~m}$ de la pregunta anterior ¿Con qué rapidez llega el carro al piso, al finalizar su recorrido? (A) $v_{f}=14,3 \frac{\mathrm{m}}{\mathrm{s}}$ (B) $v_{f}=15,3 \frac{m}{s}$ (C) $v_{f}=14,8 \frac{m}{s}$ (D) $v_{f}=15.8 \frac{\mathrm{m}}{\mathrm{s}}$ (E) $v_{j}=11,3 \frac{m}{s}$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the given data and the problem
  • Mass of the roller coaster car, \( m = 580 \, \text{kg} \)
  • Initial velocity at point A, \( v_A = 4.0 \, \frac{\text{m}}{\text{s}} \)
  • Height at point A, \( H = 12 \, \text{m} \)
  • Radius of the loop, \( R = 4.0 \, \text{m} \)
  • Height of the base of the loop, \( h = 2.0 \, \text{m} \)
  • We need to find the final velocity \( v_f \) when the car reaches the ground.
Step 2: Apply the conservation of mechanical energy

The total mechanical energy at point A (potential + kinetic) will be equal to the total mechanical energy at the final point (ground level).

\[ E_A = E_f \]

At point A: \[ E_A = \text{Potential Energy at A} + \text{Kinetic Energy at A} \] \[ E_A = m g H + \frac{1}{2} m v_A^2 \]

At the final point (ground level): \[ E_f = \text{Potential Energy at ground} + \text{Kinetic Energy at ground} \] \[ E_f = 0 + \frac{1}{2} m v_f^2 \]

Step 3: Set up the energy conservation equation

\[ m g H + \frac{1}{2} m v_A^2 = \frac{1}{2} m v_f^2 \]

Step 4: Simplify and solve for \( v_f \)

Cancel out the mass \( m \) from both sides of the equation: \[ g H + \frac{1}{2} v_A^2 = \frac{1}{2} v_f^2 \]

Multiply through by 2 to clear the fraction: \[ 2 g H + v_A^2 = v_f^2 \]

Substitute the known values: \[ 2 (9.8 \, \text{m/s}^2) (12 \, \text{m}) + (4.0 \, \text{m/s})^2 = v_f^2 \] \[ 2 (9.8) (12) + 16 = v_f^2 \] \[ 235.2 + 16 = v_f^2 \] \[ 251.2 = v_f^2 \]

Step 5: Calculate the final velocity \( v_f \)

\[ v_f = \sqrt{251.2} \] \[ v_f \approx 15.8 \, \text{m/s} \]

Final Answer

The final velocity of the car when it reaches the ground is approximately \( 15.8 \, \text{m/s} \). Therefore, the correct answer is:

\[ \boxed{D} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The function h(x)=1/(x+8) can be expressed in the form f(g(x)), where g(x)=(x+8), and f(x) is defined as: f(x)=
failedAnswered
The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, ŷ = b0 + b1 x, for predicting a woman's bone density based on her age. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant Age 47 49 50 51 58 Bone Density 360 353 336 333 310
failedAnswered
One pump can empty a pool in 7 days, whereas a second pump can empty the pool in 10 days. How long will it take the two pumps, working together, to empty the pool? (Fractional answers are OK.) The first pump's rate is per day. The second pump's rate is per day. The combined pumps rate is per day. It will take the two pumps days to empty the pool together.
failedAnswered
Which of the following supports the contention that schizophrenia is associated with brain damage? The size of the lateral ventricles increases in schizophrenic patients. The neurological symptoms noted in schizophrenia are unique to this disorder. Control subjects are more likely to show neurological symptoms. Older people, who have already lost substantial numbers of neurons, are more likely to develop schizophrenia than are younger people.
failedAnswered
A gas sample has an initial pressure of 547 mm Hg and an initial volume of 0.500 L. What is the pressure (in atm) if we decrease the volume of the sample to 225 mL? Assume the temperature and number of moles remain constant.