The image depicts a car attached to a rod of negligible mass, which is subjected to a couple moment defined by \( M = 29t^2 \, \text{N} \cdot \text{m} \), where \( t \) is the time in seconds. The engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels. The scenario requires determining the speed of the car at \( t = 8 \) seconds, given that the car initially has a speed of \( 7 \, \text{m/s} \) at \( t = 0 \). The total mass of the car and the driver is \( 158 \, \text{kg} \), and the size of the car is neglected.### Diagram Explanation:- **Components:** - A horizontal rod, \( 4 \, \text{m} \) in length, connected to a pivot point. - A car attached to the end of the rod. - A driver seated inside the car. - Arrows depicting the couple moment \( M \) and braking force \( F \).- **Labels:** - \( M = (30t^2) \, \text{N} \cdot \text{m} \) indicating the couple moment applied to the rod. - \( F = 15t \, \text{N} \) representing the braking force applied by the engine.### Problem Statement:"If the rod of negligible mass is subjected to a couple moment of \( M = 29t^2 \, \text{N} \cdot \text{m} \) where \( t \) is the time in seconds, and the engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels, determine the speed of the car at \( t = 8 \) seconds. The car at \( t = 0 \) has a speed of \( 7 \, \text{m/s} \). The total mass of the car and the driver is \( 158 \, \text{kg} \). Neglect the size of the car."

Using the angular impulse and momentum:…

4 m M (302) N-m %3D F = 15t N. If the rod of negligible mass is subjected to a couple moment of M=29t2 N;M where t is the time in seconds, and the engine of the car supplies a braking force F= 15t N to the wheels, determine the speed of the car at t= 8s. The car at t=0s a a speed of 7 m/s. The total mass of the car and the driver is 158 kg. Neglect the size of the car.

4 m M (302) N-m %3D F = 15t N. If the rod of negligible mass is subjected to a couple moment of M=29t2 N;M where t is the time in seconds, and the engine of the car supplies a braking force F= 15t N to the wheels, determine the speed of the car at t= 8s. The car at t=0s a a speed of 7 m/s. The total mass of the car and the driver is 158 kg. Neglect the size of the car.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

The image depicts a car attached to a rod of negligible mass, which is subjected to a couple moment defined by \( M = 29t^2 \, \text{N} \cdot \text{m} \), where \( t \) is the time in seconds. The engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels. The scenario requires determining the speed of the car at \( t = 8 \) seconds, given that the car initially has a speed of \( 7 \, \text{m/s} \) at \( t = 0 \). The total mass of the car and the driver is \( 158 \, \text{kg} \), and the size of the car is neglected.

### Diagram Explanation:

- **Components:**
- A horizontal rod, \( 4 \, \text{m} \) in length, connected to a pivot point.
- A car attached to the end of the rod.
- A driver seated inside the car.
- Arrows depicting the couple moment \( M \) and braking force \( F \).

- **Labels:**
- \( M = (30t^2) \, \text{N} \cdot \text{m} \) indicating the couple moment applied to the rod.
- \( F = 15t \, \text{N} \) representing the braking force applied by the engine.

### Problem Statement:

"If the rod of negligible mass is subjected to a couple moment of \( M = 29t^2 \, \text{N} \cdot \text{m} \) where \( t \) is the time in seconds, and the engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels, determine the speed of the car at \( t = 8 \) seconds. The car at \( t = 0 \) has a speed of \( 7 \, \text{m/s} \). The total mass of the car and the driver is \( 158 \, \text{kg} \). Neglect the size of the car."

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