Question

1. (a) the photograph shows a type of rollercoaster. the car is launched from point a in the photograph, accelerates to point b and then rises over point c. each loaded car has a mass of 2000 kg. c is 128 m above b. (i) state the equation linking gravitational potential energy, mass, height and gravitational field strength. (ii) show that the gravitational potential energy gained by the car when it rises from b to c is about 2.6 mj.

Explanation:

Step1: Recall the formula

The formula for gravitational potential energy is $E_p = mgh$, where $E_p$ is gravitational potential energy, $m$ is mass, $g$ is gravitational - field strength ($g = 9.8\ m/s^2$ on Earth), and $h$ is height.

Step2: Identify the values

We are given that $m = 2000\ kg$, $h=128\ m$, and $g = 9.8\ m/s^2$.

Step3: Calculate the gravitational potential energy

Substitute the values into the formula: $E_p=mgh=2000\times9.8\times128$.
$E_p = 2000\times9.8\times128=2000\times1254.4 = 2508800\ J$.
Since $1\ MJ = 10^6\ J$, then $E_p=\frac{2508800}{10^6}\ MJ\approx2.51\ MJ\approx2.6\ MJ$.

Answer:

(i) $E_p = mgh$
(ii) As shown above, by substituting $m = 2000\ kg$, $g = 9.8\ m/s^2$ and $h = 128\ m$ into $E_p=mgh$, we get $E_p=2000\times9.8\times128 = 2508800\ J\approx2.6\ MJ$.