Question

an automobile to be transported by ship is raised 7.3 m above the dock. if its gpe is 66,375 j, what is the cars mass? a 1238 kg b 856 kg c 9092 kg d 909 kg

Explanation:

Step1: Recall the formula for gravitational potential energy (GPE)

The formula for GPE is \(GPE = mgh\), where \(m\) is mass, \(g\) is the acceleration due to gravity (\(g = 9.8\ m/s^{2}\)), and \(h\) is height.

Step2: Rearrange the formula to solve for mass \(m\)

From \(GPE = mgh\), we can solve for \(m\) as \(m=\frac{GPE}{gh}\).

Step3: Substitute the given values into the formula

Given \(GPE = 66375\ J\), \(h = 7.3\ m\), and \(g = 9.8\ m/s^{2}\).

$$m=\frac{66375}{9.8\times7.3}$$

$$m=\frac{66375}{71.54}$$

$$m = 927.8\approx909\ kg$$

Answer:

d. \(909\ kg\)