40. A large bear skids to a stop at the top of a cliff with a 90 meter drop. If he has a gravitational potential energy of 55000 Joules at the top of the cliff, what is his mass?

Question

UpStudy AI · Accepted Answer

**Step 1: Write the Expression for Gravitational Potential Energy**

The gravitational potential energy is given by

$$
PE = mgh
$$

where  
$$PE$$ is the potential energy,  
$$m$$ is the mass,  
$$g$$ is the acceleration due to gravity, and  
$$h$$ is the height of the drop.

---

**Step 2: Solve for Mass $$m$$**

Rearrange the formula to solve for $$m$$:

$$
m = \frac{PE}{gh}
$$

---

**Step 3: Insert the Given Values**

We are given:
- $$PE = 55000$$ Joules,
- $$g = 9.8 \, \text{m/s}^2$$ (standard value of gravitational acceleration), and
- $$h = 90 \, \text{meters}$$.

Substitute these values into the equation:

$$
m = \frac{55000}{9.8 \times 90}
$$

---

**Step 4: Calculate the Denominator**

First, calculate the product of $$g$$ and $$h$$:

$$
9.8 \times 90 = 882
$$

---

**Step 5: Compute the Mass**

Now, substitute the value back into the equation:

$$
m = \frac{55000}{882}
$$

$$
m \approx 62.4 \, \text{kg}
$$

---

**Final Answer**

The mass of the bear is approximately $$62.4 \, \text{kg}$$.
The bear's mass is approximately 62.4 kg.

40. A large bear skids to a stop at the top of a cliff with a 90 meter drop. If he has a gravitational potential energy of 55000 Joules at the top of the cliff, what is his mass?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Physics Questions