Question

the table shows information about four objects resting at the top of a hill.
four objects at rest on a hill

object	mass (kg)	potential energy (j)
x	35	1,029
y	62	1,519
z	24	1,176

which object is on the tallest hill?
○ w
○ x
○ y
○ z

Explanation:

The formula for gravitational potential energy is \( PE = mgh \), where \( PE \) is potential energy, \( m \) is mass, \( g \) is the acceleration due to gravity (we can take \( g = 9.8 \, \text{m/s}^2 \) for simplicity), and \( h \) is the height (which corresponds to the height of the hill here). To find the height \( h \), we can rearrange the formula to \( h=\frac{PE}{mg} \). We will calculate \( h \) for each object.

Step 1: Calculate height for Object W

Given \( m_W = 50 \, \text{kg} \), \( PE_W = 980 \, \text{J} \), \( g = 9.8 \, \text{m/s}^2 \)
\( h_W=\frac{PE_W}{m_Wg}=\frac{980}{50\times9.8}=\frac{980}{490} = 2 \, \text{m} \)

Step 2: Calculate height for Object X

Given \( m_X = 35 \, \text{kg} \), \( PE_X = 1029 \, \text{J} \)
\( h_X=\frac{PE_X}{m_Xg}=\frac{1029}{35\times9.8}=\frac{1029}{343}\approx3 \, \text{m} \)

Step 3: Calculate height for Object Y

Given \( m_Y = 62 \, \text{kg} \), \( PE_Y = 1519 \, \text{J} \)
\( h_Y=\frac{PE_Y}{m_Yg}=\frac{1519}{62\times9.8}=\frac{1519}{607.6}\approx2.5 \, \text{m} \)

Step 4: Calculate height for Object Z

Given \( m_Z = 24 \, \text{kg} \), \( PE_Z = 1176 \, \text{J} \)
\( h_Z=\frac{PE_Z}{m_Zg}=\frac{1176}{24\times9.8}=\frac{1176}{235.2} = 5 \, \text{m} \)

Now we compare the heights: \( h_W = 2 \, \text{m} \), \( h_X \approx 3 \, \text{m} \), \( h_Y \approx 2.5 \, \text{m} \), \( h_Z = 5 \, \text{m} \). The largest height is for Object Z.

Answer:

Z