Final Answer:
The total mechanical energy at a is equal to the sum of the kinetic and potential energy, which is 100.0kg x 2.00m/s² + 100.0kg x 10.0m = 1,200J. The speed of the cart at b is 8.00m/s. The height of the track at c is 5.00m. The length of the track from d to g is 6.00m.
Step-by-step explanation:
The total mechanical energy at a is equal to the sum of the kinetic and potential energy. This is because the total energy of the system is conserved and the energy that is not lost due to friction, is conserved. The kinetic energy is equal to the mass of the cart multiplied by its velocity squared, which is 100.0kg x 2.00m/s² = 200J. The potential energy is equal to the mass of the cart multiplied by its height from the ground, which is 100.0kg x 10.0m = 1,000J. Therefore, the total mechanical energy at a is equal to 200J + 1,000J = 1,200J.
The speed of the cart at b is 8.00m/s. This is because the cart has been released from the top of a hill, which is 10.0m high, and it has been released with an initial velocity of 2.00m/s. The force of gravity is acting on the cart and the kinetic energy of the cart is increasing as it moves down the hill. Therefore, when the cart reaches b, its speed will be 8.00m/s.
The height of the track at c is 5.00m. This is because the height at a is 10.0m and the height at b is 5.00m. As the cart has been released from the top of the hill, the kinetic energy of the cart is increasing as it moves down the hill. As a result, the height of the track at c is 5.00m.
The length of the track from d to g is 6.00m. This is because at point d, there is a large amount of friction due to the horizontal track, which is equal to 80.4N. This friction reduces the kinetic energy of the cart and the cart eventually stops at g. As the cart can travel a maximum distance of 6.00m, the length of the track from d to g is 6.00m.