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Acceleration on Inclined Plane is defined as the value of the parallel component divided by the object's mass. It depends upon the angle of inclination and angle of repose.
- An inclined plane is a form of ramp or platform with one end elevated and forming an inclined angle.
- Acceleration is the rate of change of the velocity of a thing or object that changes with time.
- It follows the rule of changing the speed of a particular thing over time.
- The acceleration on inclined plane depends upon the inclined plane length and height.
- Galileo used the concept of an inclined plane to study the law of motion.
- It helps determine how far an object moved in a given time.
- Ramps on skateboard parks and aeroplane emergency evacuation slides are some examples of acceleration on an inclined planes.
Key Terms: Acceleration on Inclined Plane, Acceleration, Inclined Plane, Norma Force, Gravity Force, Velocity, Vector Quantities, Law of Motion, Time, Uniform Acceleration, Non-Uniform Acceleration
Acceleration on Inclined Plane
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The acceleration on an inclined plane is the value of the parallel components that are divided by the mass (m). The value of the acceleration depends upon the value of force acting on the object.
- When an object is on the inclined plane, then two forces are acting on the object.
- One force acting on the object is the gravitational force.
- The other force is the normal force, which acts perpendicular to the ramp.
These forces are not cancelled out completely otherwise the object would not accelerate. Now, tilt the coordinate system to determine the net force. This will result in the conversion of two-dimensional motion to one-dimensional motion.
- In this case, the x-axis is parallel to the inclined plane and matches the direction the object travels.
- The y-axis of the plane is perpendicular to the inclined plane.
- The force of gravity on the x-axis and y-axis is given as mg sin θ and mg cos θ, respectively.
- According to Newton's second law of motion, the force acting on an object is given by the formula:
F = ma
ma = mg sin θ
a = g sin θ
- where a is the acceleration on inclined Plane
Acceleration on Inclined Plane
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What is Acceleration?
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Acceleration is the rate of change of the velocity of a thing or object that changes with time. It is determined as vector quantities that have direction & magnitude.
- The term is equal to the difference between the initial and final velocities divided by the time.
- Acceleration can also be described as the value of change of velocity per unit of time.
- The rate of change is the ratio of the amount that changes, which means how much time it takes to change the velocity.
- Its SI unit is ms−2 and can be expressed in some other units like Gal, Standard Gravity (g), and Planck Acceleration (ap).
Types of Acceleration
There are three types of acceleration which are as follows:
Uniform Acceleration
In uniform acceleration, the velocity of a body changes but only at a constant rate within a given time interval. Consider if a car is moving in a straight line and increasing its speed within equal intervals of time; then it is called uniform acceleration.
Non-Uniform Acceleration
In non-uniform acceleration, there is a change in velocity, but it’s not in equal intervals of time. If a car is moving in a straight line, which is also increasing its speed but at unequal intervals of time, then it is non-uniform acceleration.
Average acceleration
The rate at which the velocity of a given object is changed is called its average acceleration. In this, all we need to do is divide the change in velocity by an elapsed time, and after dividing it, we will find the average of any object.
What is an Inclined Plane?
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An inclined plane is a form of platform that consists of a sloping surface. It is also known as a ramp. Its purpose is just to reduce the force that is applied to raise a load.
- When we need to raise a body vertically, we need to apply a force that is equal to the body’s weight.
- An incline is just like a surface that sets a different angle part from the right one.
- The process becomes more complicated when friction and additional forces are present.
- All forces acting on the object must be added to determine the net force.
- Some examples of inclined planes include ramps, roads, vertically, sloping, wedges, chisels, and ploughs.
Normal Force
The normal force in an inclined plane is directed upwards to the opposite direction with the force of gravity. In simple words, A normal force is not always directed in the direction that we are accustomed to.
Gravity Force
The component of the force of gravity is directed opposite to the normal force. It balances the normal force, but the parallel component of the force of gravity can’t be balanced with the help of any other force.
- It can be divided into two components- one is directed parallel towards the inclined surfaces.
- The second one is directed perpendicular towards the inclined surface.
Formula of Acceleration on an Inclined Plane
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The formula of acceleration on an inclined plane is given by:
a = g sin θ
- where a is the acceleration on inclined Plane
- g is the acceleration due to the gravity.
- When the angle increases then the force that is parallel to include also increases but the component of force decreases.
- The object is accelerated down inclined planes by uneven force.
Example of Formula of Acceleration on an Inclined PlaneExample: A ramp is placed at an angle of 10º. What is the acceleration of an object released from the top? Ans: It is given that: sin 10 = 0.173
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Things to Remember
- Acceleration on an inclined plane is determined by the value of the parallel components, which is divided by the mass.
- It is calculated with the help of gravitational force and normal force acting on an inclined plane.
- An inclined plane is a sloping surface which has one end higher than the other.
- The value of acceleration on an inclined plane is calculated when there is no friction and force acting on the object.
- Ramps & stairs are the most popular examples of inclined planes.
- Acceleration is due to gravity.
- If no starting time is given, you can assume it to be ‘0’.
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Sample Questions
Ques: What is the magnitude of acceleration? (2 marks)
Ans: Acceleration of an object is simply a rate of change of velocity. The magnitude of the acceleration tells how the velocity of an object is changed. it also tells how quickly it is changed. In simple words, the magnitude of the acceleration shows how quickly the velocity changes in a given period. For example: if your speed changes by 10m every 2 seconds then it is the magnitude acceleration.
Ques: Write the advantages of the Inclined plane? (2 marks)
Ans: there are so many advantages of an inclined plane. Here we are discussing some advantages of inclined plane:
- An inclined plane increases the distance of an object.
- It helps an object in moving by increasing the distance.
- When the slope of an inclined plane decreases, the mechanical advantage is increased.
- When you use an inclined plane to move an object, we use less force to move that object.
Ques: Ram is running at 9 m/s & skid to a halt in 4 seconds? (2 marks)
Ans: Ram went from 9m/s to 0, so the speed is decreased:
Acceleration= change in velocity (m/s) /time(s)
= -9m/s/4 s
=2.25 m/s
Ques: Describe the SI unit of acceleration? (2 marks)
Ans: Acceleration is the rate of change of the velocity within a given period. The acceleration is the quick change in the velocity of a particular object. Acceleration is written as (a). The velocity is a vector quantity and acceleration is also a vector Quantity. The SI Unit is one of them. It can be classified as:
SI unit= meters/second2 (m/s2).
It is the unit that defines a particular object of acceleration.
Ques: A boy starts his motion in a straight line at a velocity of 20 m/s, his velocity is changing at a constant rate. If he stops after the 40s, what is his acceleration? (2 marks)
Ans: The initial value of a boy = 20m/s
The final velocity = 0m/s
So the deceleration occurs which is just the opposite of the acceleration.
It can be determined as :
a= 0-20/40
=-0.5ms2
Ques: Describe Acceleration? (2 marks)
Ans: The acceleration of an object is the measurement of change in velocity. When there is a quick change in an object within a given time then it is called acceleration. The velocity of an object can be increased as well as decreased in both conditions; it is called acceleration. You can experience acceleration in your daily life by using a vehicle. For example: if you step on an accelerator & speed up the vehicle it is called acceleration.
Ques: Write any 10 examples of the Inclined plane? (3 marks)
Ans: The Incline plane can be defined as a simple machine that is used to move heavy loads over vertical obstacles. It is a plane with an angle to the horizontal. An inline plane consists of a sloping surface.
Here are the top 10 examples of Inclined planes:
- Stairs
- Slide
- Stunt pumps
- Ramps
- Mailbox
- Funnel
- Garbage Dumping
- Pyramids
- Funnel
- Moving vans
Ques: A ramp is placed at an angle of 30º. What is the acceleration of an object released from the top? (2 marks)
Ans: It is given that: sin 30 = 0.50
- g = 9.81 m/s2
- a = 9.81 x 0.50
- a = 4.90 m/s2
Ques: Kajal wants to create a ramp that accelerates objects at 8.5 m/s2 . At what angle should he set his ramp? (2 marks)
Ans: It is given that: a = 8.5 m/s2
- a = g sin θ
- 8.5 = 9.81 x sin θ
- sin θ = 0.86
- θ = 59.3 degree
Ques: An iron ball of 10 kg is kept on the table. Calculate the normal force being applied on the iron ball? (2 marks)
Ans: Given,
m = 10 kg
g = 9.8 m/s
The normal force is
Fn= mg
Fn = 10 × 9.8
Fn = 98 N
Ques: What is the magnitude of the normal force exerted on a 4kg object that is inclined at 60 degrees to the horizontal? (2 marks)
Ans: Given,
m= 4kg
g= 9.8m/s
θ = 60°
cos 30°= ½
Fn= mg cos θ
Fn= 4×9.8×1/2= 19.6N
Thus, the normal force is 9.8N.
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