Question

a cat with is on a bookcase that is 2.0 m high. the potential energy of the cat is 78j, what is the mass of the cat?
○ 7.96 kg
○ 0.2kg
○ 3.98 kg
○ 0.1kg
possible points: 0.51

Explanation:

Step1: Recall the formula for gravitational potential energy

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

Step2: Rearrange the formula to solve for mass

We need to solve \(U = mgh\) for \(m\). Dividing both sides of the equation by \(gh\) gives \(m=\frac{U}{gh}\).

Step3: Substitute the given values into the formula

We know that \(U = 78\ J\), \(h = 2.0\ m\), and \(g = 9.8\ m/s^{2}\). Substituting these values into \(m=\frac{U}{gh}\), we get \(m=\frac{78}{9.8\times2.0}\).
First, calculate \(9.8\times2.0 = 19.6\). Then \(m=\frac{78}{19.6}\approx3.98\ kg\).

Answer:

3.98 kg