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Questions and Answers
What happens to the component of velocity normal to the force acting on a body?
What happens to the component of velocity normal to the force acting on a body?
- It fluctuates randomly.
- It decreases to zero.
- It increases with time.
- It remains unchanged. (correct)
What is the average resistive force exerted by the block on the bullet?
What is the average resistive force exerted by the block on the bullet?
- 135 N
- 270 N (correct)
- 6750 N
- 540 N
What does the variable 'a' represent in the equation of motion mentioned?
What does the variable 'a' represent in the equation of motion mentioned?
- Distance traveled by the bullet.
- Acceleration of the bullet. (correct)
- Initial velocity of the bullet.
- Final velocity of the bullet.
If the bullet has a mass of 0.04 kg and comes to a stop after penetrating 0.6 m, what is the formula used to calculate its retardation?
If the bullet has a mass of 0.04 kg and comes to a stop after penetrating 0.6 m, what is the formula used to calculate its retardation?
What characterizes an impulsive force in Newtonian mechanics?
What characterizes an impulsive force in Newtonian mechanics?
What does the second law imply when the force is zero?
What does the second law imply when the force is zero?
Which statement accurately describes the nature of the second law of motion?
Which statement accurately describes the nature of the second law of motion?
What happens to a stone dropped from an accelerated train assuming no air resistance?
What happens to a stone dropped from an accelerated train assuming no air resistance?
What does 'local relation' in the context of the second law of motion signify?
What does 'local relation' in the context of the second law of motion signify?
When analyzing acceleration at an instant, which statement is accurate?
When analyzing acceleration at an instant, which statement is accurate?
What happens to the x-component of impulse after a collision?
What happens to the x-component of impulse after a collision?
What is the y-component of the impulse after the collision?
What is the y-component of the impulse after the collision?
In which direction is the force applied to the wall by the ball?
In which direction is the force applied to the wall by the ball?
How is the direction of force on the wall categorized in both cases?
How is the direction of force on the wall categorized in both cases?
What results from applying Newton’s third law in the context of the wall and the ball?
What results from applying Newton’s third law in the context of the wall and the ball?
What is the relationship between the coefficients of static and kinetic friction?
What is the relationship between the coefficients of static and kinetic friction?
When a body is momentarily at rest, what can be said about the force acting on it?
When a body is momentarily at rest, what can be said about the force acting on it?
What does the second law of motion, F = ma, represent?
What does the second law of motion, F = ma, represent?
Which statement about force direction is correct?
Which statement about force direction is correct?
When a stone is released from an accelerated train, what happens to its forces?
When a stone is released from an accelerated train, what happens to its forces?
What is the formula for the maximum speed of a car on a banked road?
What is the formula for the maximum speed of a car on a banked road?
What happens at the optimum speed on a banked road?
What happens at the optimum speed on a banked road?
What is the optimum speed (vo) formula for a banked road?
What is the optimum speed (vo) formula for a banked road?
If the coefficient of static friction (µs) equals zero, what is the condition for parking on a banked road?
If the coefficient of static friction (µs) equals zero, what is the condition for parking on a banked road?
What is the effect of driving at speed less than optimum speed (vo) on a banked road?
What is the effect of driving at speed less than optimum speed (vo) on a banked road?
What is the maximum permissible speed (vmax) equation for a car on a banked road?
What is the maximum permissible speed (vmax) equation for a car on a banked road?
If the radius of a turn is increased, what effect does it have on the maximum speed (vmax) on a banked road?
If the radius of a turn is increased, what effect does it have on the maximum speed (vmax) on a banked road?
What does the angle θ determine in the context of a banked road?
What does the angle θ determine in the context of a banked road?
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Study Notes
Second Law of Motion
- The equation F = ma highlights the relationship between force, mass, and acceleration, establishing that if F = 0, then a = 0, aligning with Newton's first law.
- The second law is a vector law, represented by three equations for each spatial component (x, y, z).
- Acceleration at a specific instant depends solely on the force acting at that exact moment, independent of past motion.
- A dropped stone from an accelerating train will exhibit no horizontal force or acceleration, assuming air resistance is negligible.
Bullet Example
- If a bullet of mass 0.04 kg and speed of 90 m/s enters a block and travels 60 cm before stopping, the average resistive force can be calculated.
- The bullet's retardation is determined using the equation a = -u²/2s, leading to a calculation of a = -6750 m/s².
- The resistance force applied by the block on the bullet is F = ma = 0.04 kg × 6750 m/s² = 270 N.
Impulse and Collision
- In a collision, impulses can be calculated using the components of the momentum and the geometric angles involved.
- For impacts normal to a surface, the impulse effects will affect the change in momentum directly.
- The direction of force is normal to the wall in both inclined and non-inclined cases, despite prior assumptions about force orientations.
Banked Roads and Ideal Speed
- On a banked road, centripetal force arises from the components of the normal force and frictional force.
- The optimum speed (vo) for a vehicle to negotiate a banked curve is derived as vo = (Rg tan θ)½, with R representing the radius and θ the angle of the bank.
- With no need for friction at vo, driving at this speed minimizes tire wear.
Frictional Forces
- The relationship between static (µs) and kinetic friction (µk) illustrates that static friction is generally higher, allowing for different behaviors when engaging with surfaces.
- The conditions for maximum static friction can be expressed as fs ≤ fs_max = µs R, where R is the normal force.
Key Considerations in Mechanics
- Force is not always directed along the line of motion; it may act in various orientations relative to velocity, but is always parallel to acceleration.
- Even if an object is stationary (v = 0), it does not imply zero force or acceleration at that moment, as seen when a ball reaches its peak height under the influence of gravity.
- Current force acting on a body is determined by the circumstances at that moment, not its previous motion history.
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