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A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.?
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A constant force acts for 5s on a mass of 100kg initially at rest and ...
Given Information
- Mass (m) = 100 kg
- Initial velocity (u) = 0 m/s (object is at rest)
- Time during which force acts (t1) = 5 s
- Displacement in the next 5 s (s) = 1000 m
Acceleration Calculation
1. **Determine the total time of motion:**
- Total time (T) = 5s (force acting) + 5s (force not acting) = 10s
2. **Using the formula for displacement when acceleration is constant:**
- The displacement during the first 5s (s1) can be expressed as:
\[ s_1 = ut + \frac{1}{2} a t^2 \]
- Since u = 0, it simplifies to:
\[ s_1 = \frac{1}{2} a (5)^2 = \frac{25a}{2} \]
3. **Displacement during the second phase (no force acting):**
- The final velocity (v) after 5s is:
\[ v = u + at = 0 + 5a = 5a \]
- The displacement (s2) during the next 5s:
\[ s_2 = vt + \frac{1}{2} a t^2 = (5a)(5) + \frac{1}{2} (0)(5^2) = 25a \]
4. **Total displacement equation:**
- Total displacement = s1 + s2 = 1000 m
- So, \[ \frac{25a}{2} + 25a = 1000 \]
- Simplifying gives:
\[ \frac{75a}{2} = 1000 \]
\[ a = \frac{2000}{75} = \frac{400}{15} \approx 26.67 \, \text{m/s}^2 \]
Force Calculation
1. **Using Newton’s second law (F = ma):**
- Magnitude of the force (F) is:
\[ F = m \cdot a = 100 \cdot 26.67 \approx 2667 \, \text{N} \]
Conclusion
- The magnitude of the constant force acting on the mass is approximately **2667 N**.
- Mass (m) = 100 kg
- Initial velocity (u) = 0 m/s (object is at rest)
- Time during which force acts (t1) = 5 s
- Displacement in the next 5 s (s) = 1000 m
Acceleration Calculation
1. **Determine the total time of motion:**
- Total time (T) = 5s (force acting) + 5s (force not acting) = 10s
2. **Using the formula for displacement when acceleration is constant:**
- The displacement during the first 5s (s1) can be expressed as:
\[ s_1 = ut + \frac{1}{2} a t^2 \]
- Since u = 0, it simplifies to:
\[ s_1 = \frac{1}{2} a (5)^2 = \frac{25a}{2} \]
3. **Displacement during the second phase (no force acting):**
- The final velocity (v) after 5s is:
\[ v = u + at = 0 + 5a = 5a \]
- The displacement (s2) during the next 5s:
\[ s_2 = vt + \frac{1}{2} a t^2 = (5a)(5) + \frac{1}{2} (0)(5^2) = 25a \]
4. **Total displacement equation:**
- Total displacement = s1 + s2 = 1000 m
- So, \[ \frac{25a}{2} + 25a = 1000 \]
- Simplifying gives:
\[ \frac{75a}{2} = 1000 \]
\[ a = \frac{2000}{75} = \frac{400}{15} \approx 26.67 \, \text{m/s}^2 \]
Force Calculation
1. **Using Newton’s second law (F = ma):**
- Magnitude of the force (F) is:
\[ F = m \cdot a = 100 \cdot 26.67 \approx 2667 \, \text{N} \]
Conclusion
- The magnitude of the constant force acting on the mass is approximately **2667 N**.
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A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.?
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A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.?.
A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A constant force acts for 5s on a mass of 100kg initially at rest and ceases to act. It in the next 5s the mass has displacement of 1000m find magnitude of force.?.
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