Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

You wish to make a simple amusement park ride in which a steel-wheeled roller-coaster car travels down one long slope, where rolling friction is negligible, and later slows to a stop through kinetic friction between the roller coaster's locked wheels sliding along a horizontal plastic (polystyrene) track. Assume the roller-coaster car (filled with passengers) has a mass of 743.0 kg and starts 83.4 m above the ground. (a) Calculate how fast the car is going when it reaches the bottom of the hill. m/s (b) How much does the thermal energy of the system change during the stopping motion of the car

Sagot :

Answer:

(a) The car is going approximately 40.43 m/s at the bottom of the hill

(b) The thermal energy will increase by 607,268.76 J

Explanation:

In the question, we have;

The height of the roller coaster above ground = 83.4 m

The mass of the roller coaster, m = 743.0 kg

(a) By the conservation of energy principle, we have;

The potential energy at the top of the hill, P.E., is equal to the kinetic energy at the bottom of the hill, K.E.

∴ P.E. = K.E.

P.E. = m·g·h

Where;

m = The mass of the roller coaster = 743.0 kg

g = The acceleration due to gravity = 9.8 m/s²

h = The height of the roller coaster = 83.4 m

Therefore, we have;

P.E. = 743.0 kg × 9.8 m/s² × 83.4 m = 607,268.76 J

P.E. = 607,268.76 J

K.E. = 1/2·m·v²

∴ K.E. = 1/2 × 743.0 kg × v²

P.E. = K.E.

∴ P.E. = K.E. = 607,268.76 J

1/2 × 743.0 kg × v² = 607,268.76 J

v² = 607,268.76 J/(1/2 × 743.0 kg) = 1,634.64 m²/s²

v = √(1,634.64 m²/s²) ≈ 40.43 m/s

(b) Given that the material wheel moves along polystyrene track, the sound released will be minimal and almost all the kinetic energy will be converted to heat energy when the train stops, therefore, the thermal energy will increase by K.E. = 607,268.76 J

pstnonsonjoku

The thermal energy change of the system is 624,492 J.

We know that in the roller coaster, there is an energy transformation from gravitational potential energy to kinetic energy. As such we can write;

mgh = 1/2mv^2

Where we cancel out the mass from both sides, we are left with;

gh=0.5v^2

v= √gh/0.5

v = √10 × 83.4 m/0.5

v = 41 ms-1

Now the kinetic energy is converted also into heat energy hence;

Thermal energy change of the system = 1/2 mv^2 = 0.5 × 743.0 kg × ( 41 ms-1)^2 = 624,492 J

Learn more about energy: https://brainly.com/question/1195122

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.