Motion under Gravity Notes

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Motion under Gravity Notes. Gravity is one of the four fundamental forces of nature, and its effects can be seen in everyday life. From the Earth orbiting the Sun to the movement of the planets around their stars, gravity is the mysterious force that keeps the universe in motion.

In this series of notes, we’ll explore the basics of gravity and its effects on motion. From Newton’s laws of motion to the motion of planets, we’ll investigate the mysteries of gravity and learn how it affects the motion of objects.Lets take drive into the short and crisp notes on Motion under Gravity Notes

Motion under Gravity Notes

The motion under gravity refers to the movement of an object that is subject to the force of gravity. Here are some important concepts to keep in mind when studying motion under gravity.

Acceleration due to Gravity

Acceleration due to gravity is the acceleration experienced by an object when it falls towards the earth. It is denoted by the letter ‘g’ and has a value of approximately 9.8 m/s^2. The value of ‘g’ is constant at all points on the surface of the earth, and it is the same for all objects regardless of their mass.

Free Fall

Free fall refers to the motion of an object that is falling under the influence of gravity alone. In free fall, an object’s velocity increases as it falls towards the ground. When an object is in free fall, the only force acting on it is the force of gravity, and it accelerates at a constant rate of ‘g’ towards the ground.

Equations of Motion under Gravity

The following equations can be used to describe the motion of an object under gravity:

v = u + gt
s = ut + 0.5gt^2
v^2 = u^2 + 2gs

where:

v = final velocity
u = initial velocity
g = acceleration due to gravity
t = time taken
s = distance travelled

These equations can be used to calculate the displacement, velocity, and acceleration of an object under gravity. The first equation gives the final velocity of the object, the second equation gives the displacement of the object, and the third equation gives the final velocity of the object squared.

Projectiles

A projectile is any object that is thrown into the air and then moves under the influence of gravity alone. The motion of a projectile can be described by the following equations:

Range = u^2 sin(2θ)/g
Time of flight = 2u sinθ/g
Maximum height = u^2 sin^2θ/2g

where:

θ = angle of projection
u = initial velocity
g = acceleration due to gravity

These equations can be used to calculate the range, time of flight, and maximum height of a projectile. The range is the horizontal distance travelled by the projectile, the time of flight is the time taken by the projectile to reach the ground, and the maximum height is the highest point reached by the projectile.

I hope these notes are more detailed and helpful for you. If you have any further questions or need more information, feel free to ask.

Basic Numericals on Motion under Gravity

Sure, here are some basic numerical problems on motion under gravity that involve solving for various parameters:

A ball is thrown vertically upward with an initial velocity of 20 m/s. How high does it rise before it starts falling back down?
Solution:
Using the formula for vertical displacement, we have:
v_f^2 = v_i^2 + 2gh

where v_f is the final velocity (0 m/s), v_i is the initial velocity (20 m/s), g is the acceleration due to gravity (-9.81 m/s^2), and h is the maximum height reached by the ball.
Solving for h, we get:
h = (v_f^2 – v_i^2)/(2g)
h = (0 – 20^2)/(2*(-9.81))
h = 20.2 meters

A stone is dropped from a height of 100 meters. How long does it take to reach the ground?
Solution:
Using the formula for vertical displacement, we have:
h = v_it + (1/2)gt^2
where v_i is the initial velocity (0 m/s), g is the acceleration due to gravity (-9.81 m/s^2), and h is the height from which the stone is dropped.

Solving for t, we get:
t = sqrt((2h)/g)
t = sqrt((2100)/9.81)
t = 4.52 seconds

A ball is thrown horizontally from the top of a cliff with a speed of 10 m/s. How far from the base of the cliff will the ball hit the ground if the cliff is 50 meters high?
Solution:
The horizontal motion of the ball is independent of its vertical motion, so we can use the formula for horizontal displacement, which is:
d = v_xt
where d is the horizontal distance traveled, v_x is the horizontal velocity (10 m/s), and t is the time taken for the ball to hit the ground.


Using the formula for vertical displacement, we can find the time taken for the ball to hit the ground:
h = (1/2)gt^2
where h is the height of the cliff (50 meters).
Solving for t, we get:
t = sqrt((2h)/g)
t = sqrt((2*50)/9.81)
t = 3.19 seconds
Now, using the formula for horizontal displacement, we have:
d = v_xt
d = 10 m/s * 3.19 seconds
d = 31.9 meters
Therefore, the ball will hit the ground 31.9 meters from the base of the cliff.

What is motion under gravity

Motion under gravity refers to the movement of an object influenced by the force of gravity. When an object is subject to gravity and no other significant forces, it will experience a specific type of motion known as free fall or projectile motion.

In the case of free fall, an object is dropped or falls vertically near the surface of the Earth. Ignoring air resistance, the only force acting on the object is the gravitational force pulling it downward. The acceleration due to gravity near the Earth’s surface is approximately 9.8 meters per second squared (m/s²) and is denoted by the symbol “g”. This means that in free fall, the object’s velocity increases by 9.8 m/s for every second it falls.

During projectile motion, an object is launched into the air at an angle or given an initial velocity that has both horizontal and vertical components. The horizontal component remains unaffected by gravity, while the vertical component is influenced by gravity. The object follows a curved trajectory, called a parabola.

In both cases, the motion under gravity can be described using equations of motion and principles of physics. These equations allow us to calculate various aspects of the motion, such as the object’s displacement, velocity, time of flight, and maximum height reached.

It’s important to note that in reality, factors like air resistance and the variation of gravitational acceleration with altitude can affect the motion. However, for most practical purposes, these effects are often neglected when studying motion under gravity in simple scenarios.

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What is the equation of motion under gravity

The equations of motion under gravity can be derived using the principles of physics, specifically the laws of motion. For an object in free fall or projectile motion near the Earth’s surface, the following equations can be used:

  1. Displacement equation:
    • In the vertical direction (y-axis):
      • y = v₀t + (1/2)gt²
      • where:
        • y is the vertical displacement (height) of the object at time t,
        • v₀ is the initial vertical velocity of the object,
        • g is the acceleration due to gravity (approximately 9.8 m/s²),
        • t is the time elapsed.
    • In the horizontal direction (x-axis):
      • x = v₀x * t
      • where:
        • x is the horizontal displacement of the object at time t,
        • v₀x is the initial horizontal velocity of the object,
        • t is the time elapsed.
  2. Velocity equations:
    • In the vertical direction (y-axis):
      • vy = v₀y + gt
      • where:
        • vy is the vertical component of velocity at time t,
        • v₀y is the initial vertical velocity of the object,
        • g is the acceleration due to gravity.
    • In the horizontal direction (x-axis):
      • vx = v₀x
      • where:
        • vx is the horizontal component of velocity at any time t,
        • v₀x is the initial horizontal velocity of the object.
  3. Time of flight:
    • The time of flight (T) is the total time it takes for the object to reach the ground or complete its trajectory.
    • It can be found by setting the vertical displacement y to zero in the displacement equation:
      • 0 = v₀y * T + (1/2)gT²
      • Solving this quadratic equation will give the time of flight.

These equations allow you to calculate various parameters of the motion, such as the object’s displacement, velocity, time of flight, and maximum height reached, given appropriate initial conditions.

Motion under gravity questions with answers

 What is the acceleration due to gravity on the surface of the Earth?

Answer: The acceleration due to gravity on the surface of the Earth is approximately 9.8 meters per second squared (m/s²

 What is the formula to calculate the distance traveled by an object in free fall?

Answer: The formula to calculate the distance traveled by an object in free fall is given by d = 1/2 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is the time.

 What is the velocity of an object in free fall after 3 seconds of falling?

Answer: The velocity of an object in free fall after 3 seconds of falling can be calculated using the formula v = g * t, where v is the velocity, g is the acceleration due to gravity, and t is the time. So, the velocity would be 9.8 m/s² * 3 s = 29.4 m/s.

Can an object have a negative velocity during free fall?

Answer: Yes, an object can have a negative velocity during free fall. If the object is moving upward against the direction of gravity, its velocity will be negative.

What is the relationship between the mass of an object and its acceleration during free fall?

Answer: The mass of an object does not affect its acceleration during free fall. All objects, regardless of their mass, experience the same acceleration due to gravity.

What happens to the velocity of an object in free fall as it falls towards the Earth?

Answer: The velocity of an object in free fall increases as it falls towards the Earth. It accelerates at a constant rate of approximately 9.8 m/s² due to gravity.

 How does air resistance affect the motion of objects in free fall?

Answer: Air resistance opposes the motion of objects in free fall. It increases as the object’s velocity increases. At higher velocities, air resistance can balance out the force of gravity, resulting in a constant velocity called terminal velocity.

Can an object in free fall have multiple forces acting on it? If so, give an example.

Answer: Yes, an object in free fall can have multiple forces acting on it. For example, if an object is falling and experiencing air resistance, there will be two forces acting on it: the force of gravity pulling it downward and the force of air resistance pushing against it.

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How does the altitude affect the acceleration due to gravity?

Answer: The acceleration due to gravity decreases with increasing altitude. As an object moves higher above the Earth’s surface, the gravitational pull decreases, resulting in a slightly lower acceleration due to gravity.

 What is the relationship between the time of flight and the maximum height reached by an object in projectile motion?

Answer: The time of flight is directly proportional to the maximum height reached by an object in projectile motion. The longer an object stays in the air, the higher it will reach.

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