Physics: Newton's Second Law

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Questions and Answers

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?

135 N

270 N (correct)

6750 N

540 N

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?

a = -u^2 / (2s) Signup and view all the answers

What characterizes an impulsive force in Newtonian mechanics?

It is large and acts for a short time. Signup and view all the answers

What does the second law imply when the force is zero?

The object remains at rest or continues to move at a constant speed. Signup and view all the answers

Which statement accurately describes the nature of the second law of motion?

It is a vector law equivalent to three equations in vector components. Signup and view all the answers

What happens to a stone dropped from an accelerated train assuming no air resistance?

It has no horizontal acceleration or force. Signup and view all the answers

What does 'local relation' in the context of the second law of motion signify?

Force at a point is determined by the acceleration produced in that instant. Signup and view all the answers

When analyzing acceleration at an instant, which statement is accurate?

Force at that instant determines acceleration, ignoring any prior forces. Signup and view all the answers

What happens to the x-component of impulse after a collision?

It flips sign. Signup and view all the answers

What is the y-component of the impulse after the collision?

It remains the same. Signup and view all the answers

In which direction is the force applied to the wall by the ball?

Normal to the wall in the positive x direction. Signup and view all the answers

How is the direction of force on the wall categorized in both cases?

Normal to the wall. Signup and view all the answers

What results from applying Newton’s third law in the context of the wall and the ball?

The force on the wall is opposite to the force applied by the ball. Signup and view all the answers

What is the relationship between the coefficients of static and kinetic friction?

µk is less than µs. Signup and view all the answers

When a body is momentarily at rest, what can be said about the force acting on it?

The force can still be non-zero. Signup and view all the answers

What does the second law of motion, F = ma, represent?

F is the net force due to external agencies. Signup and view all the answers

Which statement about force direction is correct?

Force may also act at an angle to the direction of motion. Signup and view all the answers

When a stone is released from an accelerated train, what happens to its forces?

Only the vertical force of gravity acts on the stone. Signup and view all the answers

What is the formula for the maximum speed of a car on a banked road?

v max = (µ + tan θ) Rg Signup and view all the answers

What happens at the optimum speed on a banked road?

The frictional force is not required at all. Signup and view all the answers

What is the optimum speed (vo) formula for a banked road?

vo = (R g tan θ) 1/2 Signup and view all the answers

If the coefficient of static friction (µs) equals zero, what is the condition for parking on a banked road?

tan θ must be less than or equal to µs. Signup and view all the answers

What is the effect of driving at speed less than optimum speed (vo) on a banked road?

Frictional force acts down the slope. Signup and view all the answers

What is the maximum permissible speed (vmax) equation for a car on a banked road?

vmax = (µ + tan θ) Rg / (1 - µs tan θ) Signup and view all the answers

If the radius of a turn is increased, what effect does it have on the maximum speed (vmax) on a banked road?

vmax increases. Signup and view all the answers

What does the angle θ determine in the context of a banked road?

The balance of forces involved. Signup and view all the answers

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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Description

This quiz explores key concepts of Newton's Second Law, focusing on the relationship between force and acceleration. It highlights how forces act on objects in different scenarios, such as in an accelerated train. Test your understanding of fundamental physics principles with this quiz.