A mass m is traveling at an initial speed . it is brought to rest in a di
ff 62.5 m by a force of 15.0 N . The mass is:

Ask by Greene Barrett. in Jordan

Dec 28,2024

Question

A mass m is traveling at an initial speed $$ v_{i}=25.0 \mathrm{~m} / \mathrm{s} $$. it is brought to rest in a di ff 62.5 m by a force of 15.0 N . The mass is:

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To determine the mass $$ m $$ of the object, we can use the **work-energy principle**, which states that the work done by the force is equal to the change in the object's kinetic energy.

### Given:
- **Initial velocity** ($$ v_i $$) = 25.0 m/s
- **Final velocity** ($$ v_f $$) = 0 m/s (since it's brought to rest)
- **Distance** ($$ d $$) = 62.5 m
- **Force** ($$ F $$) = 15.0 N (acting opposite to the direction of motion)

### Steps to Calculate Mass:

1. **Calculate the Work Done by the Force:**
   
   The work done $$ W $$ by the force is:
   $$
   W = F \times d
   $$
   Since the force is acting opposite to the motion, it does negative work:
   $$
   W = -F \times d
   $$

2. **Change in Kinetic Energy:**
   
   The change in kinetic energy ($$ \Delta KE $$) is:
   $$
   \Delta KE = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2
   $$
   Since $$ v_f = 0 $$:
   $$
   \Delta KE = -\frac{1}{2} m v_i^2
   $$

3. **Set Work Equal to Change in Kinetic Energy:**
   
   $$
   -F \times d = -\frac{1}{2} m v_i^2
   $$
   Simplifying:
   $$
   F \times d = \frac{1}{2} m v_i^2
   $$

4. **Solve for Mass $$ m $$:**
   
   $$
   m = \frac{2 F d}{v_i^2}
   $$

5. **Plug in the Values:**
   
   $$
   m = \frac{2 \times 15.0 \, \text{N} \times 62.5 \, \text{m}}{(25.0 \, \text{m/s})^2}
   $$
   
   $$
   m = \frac{1875}{625} = 3 \, \text{kg}
   $$

### **Answer:**
The mass $$ m $$ is **3 kg**.
The mass $$ m $$ is **3 kg**.

A mass m is traveling at an initial speed . it is brought to rest in a di
ff 62.5 m by a force of 15.0 N . The mass is:

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A mass m is traveling at an initial speed . it is brought to rest in a di ff 62.5 m by a force of 15.0 N . The mass is: