Question

PLEASE HELP!!!! OFFERING 99 POINTS!!

The Gravitational PE (U) depends on three things: the object’s mass (m), its height (h), and gravitational acceleration (g), which is 9.81 m/s^2 on Earth’s surface. Set the mass of the car to 50.0 grams, then set the three hills to the following heights: Hill 1 - 90.0 cm, Hill 2 - 65.0 cm, Hill 3 - 20.0 cm. Calculate the difference in Gravitational Potential Energy from the top of Hill 1 to the top of Hill 3. Show all work.

Answer 1

The question has provided the most important equation:

The Gravitational PE (U) = the object’s mass (m) x its height (h) x gravitational acceleration (g)

Only trick here is the unit for each variable: PE (U) is in J which is kg-m/s^2-m; mass (m) is kg; gravity (g) is m/s^2 and height (h) is m.

With the conversion factors of gram=1/1000kg and cm=1/100m, U can be calculated as follows:

Hill 1=(50/1000)x(90/100)x9.81=0.44J

Hill 2=(50/1000)x(65/100)x9.81=0.32J

Hill 3=(50/1000)x(20/100)x9.81=0.098J

The difference in PE from Hill 1 to Hill 3

=0.44-0.098

=0.342J

Answer 2

The Gravitational PE (U) depends on three things: the object’s mass (m), its height (h), and gravitational acceleration (g), which is 9.81 m/s^2 on Earth’s surface.

so U = mgh = 9.81mh on earth

mass of the car = 50.0 grams = 0.05kg

height, h:

Hill 1 = 90.0 cm = 0.9m,

Hill 2 = 65.0 cm = 0.65m,

Hill 3 = 20.0 cm = 0.2m

substitute into eqn U = mgh

U @ top of Hill 1 = 0.05*9.81*0.9 = 0.4415J

U @ top of Hill 2 = 0.05*9.81*0.65 = 0.3188J

U @ top of Hill 3 = 0.05*9.81*0.2 = 0.0981J

difference in Gravitational Potential Energy from the top of Hill 1 to the top of Hill 3 = 0.4415 - 0.0981

= 0.3434J where J is the unit for energy, Joules