https://file.aiquickdraw.com/mathbot/file/1729898359762wzhx2ndv.jpg

We are given:

- Momentum, \( p = 29.6 \, \text{kg} \cdot \text{m/s} \)
- Kinetic energy, \( KE = 277 \, \text{J} \)

We need to find:

(a) The speed of the object \( v \) in meters per second.

(b) The mass of the object \( m \) in kilograms.

### Key Formulas:
1. Momentum: \( p = m \cdot v \)
2. Kinetic energy: \( KE = \frac{1}{2} m v^2 \)

### Step 1: Relating momentum and kinetic energy
We can use the kinetic energy formula and the fact that momentum is related to speed to derive \( v \) and \( m \).

From momentum:
\[ v = \frac{p}{m} \]

Substitute into the kinetic energy formula:
\[
KE = \frac{1}{2} m v^2 = \frac{1}{2} m \left(\frac{p}{m}\right)^2
\]

Simplifying:
\[
KE = \frac{p^2}{2m}
\]

Now, solve for mass \( m \):
\[
m = \frac{p^2}{2KE}
\]

### Step 2: Plug in the values
Using the given values:
- \( p = 29.6 \, \text{kg} \cdot \text{m/s} \)
- \( KE = 277 \, \text{J} \)

\[
m = \frac{(29.6)^2}{2 \times 277}
\]
\[
m = \frac{876.16}{554}
\]
\[
m \approx 1.582 \, \text{kg}
\]

### Step 3: Solve for speed \( v \)
Now that we know \( m \), we can find the speed \( v \):
\[
v = \frac{p}{m} = \frac{29.6}{1.582}
\]
\[
v \approx 18.71 \, \text{m/s}
\]

### Final Answers:
(a) Speed of the object \( v \approx 18.71 \, \text{m/s} \)

(b) Mass of the object \( m \approx 1.582 \, \text{kg} \)

Would you like more details on any of these calculations?

Here are 5 related questions:
1. What is the relationship between momentum and kinetic energy?
2. Can momentum and kinetic energy be conserved simultaneously in all collisions?
3. How would the speed change if the kinetic energy doubled but momentum remained constant?
4. How does an increase in mass affect the kinetic energy if the speed remains unchanged?
5. What is the difference between linear momentum and angular momentum?

**Tip:** To solve for unknown quantities in mechanics, using a combination of formulas often reveals helpful relationships between variables.

An object is traveling such that it has a momentum of magnitude 29.6 kg·m/s and a kinetic energy of 277 J. Determine the speed and mass of the object.

Learn how to calculate the speed and mass of an object using its momentum (29.6 kg·m/s) and kinetic energy (277 J). This problem explores key physics concepts such as momentum, kinetic energy, and their relationships. Suitable for high school students (Grades 10-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation