Question

directions: solve the following word problems using the potential energy formula (be sure to show your work). p.e = weight x height

1. a cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat - top. if the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat - top?
2. a 75 - kg refrigerator is located on the 70th floor of a skyscraper (300 meters above the ground). what is the potential energy of the refrigerator?
3. there is a bell at the top of a tower that is 45 m high. the bell weighs 190 kg. what is the potential energy of the bell?
4. the potential energy of an apple is 6 joules. the apple is 3 m high in a tree. what is the mass of the apple?
5. the potential energy of a 40 kg cannon ball is 14000 j. how high was the cannon ball to have this much potential energy?

Explanation:

Step1: Recall weight formula

Weight = mass $\times$ gravitational - acceleration. On Earth, gravitational - acceleration $g = 9.8\ m/s^{2}$. The potential - energy formula can be written as $P.E=mass\times g\times height$.

Step2: Solve problem 6

Given mass $m = 3.0\ kg$ and height $h = 0.45\ m$.
$P.E=m\times g\times h=3.0\times9.8\times0.45$
$P.E = 13.23\ J$.

Step3: Solve problem 7

Given mass $m = 75\ kg$ and height $h = 300\ m$.
$P.E=m\times g\times h=75\times9.8\times300$
$P.E=220500\ J$.

Step4: Solve problem 8

Given mass $m = 190\ kg$ and height $h = 45\ m$.
$P.E=m\times g\times h=190\times9.8\times45$
$P.E = 83790\ J$.

Step5: Solve problem 9

Given $P.E = 6\ J$ and height $h = 3\ m$.
Since $P.E=m\times g\times h$, then $m=\frac{P.E}{g\times h}$.
$m=\frac{6}{9.8\times3}\approx0.204\ kg$.

Step6: Solve problem 10

Given mass $m = 40\ kg$ and $P.E = 14000\ J$.
Since $P.E=m\times g\times h$, then $h=\frac{P.E}{m\times g}$.
$h=\frac{14000}{40\times9.8}\approx35.71\ m$.

Answer:

1. $13.23\ J$
2. $220500\ J$
3. $83790\ J$
4. $0.204\ kg$
5. $35.71\ m$