Step-by-Step Solution: Finding the Gravitational Force on a Roller
Introduction
In this experiment, students need to determine the downward force along an inclined plane. The downward force is acting on a roller as a result of gravity. Gravity is a force that always pulls each object in a downward direction.
You can find the gravitational pull upon the object in this inclined plane experiment. The angle of inclination is denoted as θ.
This is the angle that you need to determine and study its relationship with the gravitational pull. This is the article that can give you the liberty to verify and understand the truth.
Definition of Gravitational Pull
Gravitational pull is a downward force that attracts every object’s downwards to the centre of the earth. Higher mass objects have higher gravity. This is a universal force of attraction that is seen among all matters.
In this experiment, you will notice a force that is acting on a roller due to the gravitational pull of the earth.
Aim of the Experiment
Students are here to find the downward force which is acting along an inclined plane. You can also determine the relationship between force and the angle of inclination (sin θ) with the help of graphs.
Some of the important apparatus or materials are mentioned below:
The inclined plane that comes with a protractor and a pulley
Weight box
Pan and thread
Roller
Spring balance
Spirit level
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Principle of the Experiment
In the above picture, students can notice a roller that has a mass of M1. This roller is kept over an inclined plane. The inclined plane has made an angle θ of with the horizontal.
It gives rise to an upward force that acts along the body over the inclined place. The body is always adjusting the suspended weights.
One end of the string is linked to the mass via a pulley. This pulley is fixed and does not form the top of the plane. A farce is applied on the mass M1, and it helps the mass to move with a constant velocity ‘v’.
An expression for the above is developed. It is represented as:
W = M1 g sin θ – fr
Here, W = Total tension in the string (Also, W = weight suspended)
M1 = mass of the roller
fr = force of friction because of rolling of the object
Experiment Procedure
Prepare a plane with some angle of inclination. Then keep all necessary objects such as masses and a roller as per the given figure. Arrange all apparatus as shown in the diagram.
Arrange a pulley with the system of experiment and make it friction-proof. You can try to lubricate the pulley by using a machine whenever necessary.
Students must focus on the adjustment of the suspended weight i.e., ‘W’. Make sure that the roller remains at the tip of the inclined during its rest condition.
Now, start the decreasing of the mass gradually. You can do so by eliminating the mass out of the pan. You will notice that the roller is starting in a downward direction with a constant velocity. Now, it is time to note down the value of W and the angle θ.
Let’s repeat step – 4 for two to three times for different values of θ and fill those details in a table for further observations.
Observation
Here, M1 g = Mass of the roller
M2 g = Mass of the pan
Students should write down up to three results for finding the appropriate output of the force.
Plotting Graph
After the result, a graph has been plotted between sin θ and force that shows a straight line.
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Conclusion
It is concluded that we can find the downward force with the help of the table along an inclined plane. Also, the graph shows that W is directly proportional to sin θ. Here, the angle of inclination is θ.
Mock Tests
1. What is the Relation Between the Angle of Inclination and the Downward Force in the above Experiment?
Ans: A relation that is developed between the angle of inclination and the downward is force is mg sin θ.
If you take the mass as constant, then W ∝ Sin θ.
2. How Do You Define an Inclined Plane?
Ans: An inclined plane can be made out of a wooden plane. When you place a glass sheet above the plane, it acts as an inclined plane. This has to be done to make the surface smooth. It has made an angle θ with the ground.
3. Write Down Some Applications of the Inclined Plane.
Ans: Here is the list of applications of the inclined planes:
Ramps of your house
The method is used in ladder
A plank used at the back of the truck for lifting heavy goods
FAQs on Calculate Downward Force on an Inclined Plane Due to Gravity
1. What is the formula to calculate the downward force on an object along an inclined plane due to gravity?
The formula to calculate the downward force acting parallel to an inclined plane is F_parallel = mg sin(θ). Here, 'm' is the mass of the object, 'g' is the acceleration due to gravity (approximately 9.8 m/s²), and 'θ' (theta) is the angle of inclination of the plane with the horizontal.
2. Why is the force of gravity (weight) resolved into two components for an object on an inclined plane?
The force of gravity (weight, mg) always acts vertically downwards. On an inclined plane, this force is neither parallel nor perpendicular to the surface. To analyse the object's motion along the plane, we resolve its weight into two perpendicular components:
- mg sin(θ): The component acting parallel to the inclined plane, which tries to slide the object down.
- mg cos(θ): The component acting perpendicular to the plane, which presses the object against the surface.
3. What is the difference between the downward gravitational force and the normal force on an inclined plane?
The key difference lies in their direction and magnitude. The downward gravitational force (weight, mg) acts straight down towards the centre of the Earth. The normal force (N) is the support force exerted by the plane's surface on the object, and it always acts perpendicular to the surface. On an inclined plane, the normal force is equal to the perpendicular component of gravity, so N = mg cos(θ), not the full weight mg.
4. How does changing the angle of inclination affect the downward force pulling an object along the plane?
The downward force along the plane is directly proportional to the sine of the angle of inclination (F ∝ sin(θ)). This means:
- If you increase the angle (θ), sin(θ) increases, and the downward force becomes stronger, causing the object to slide down faster.
- If you decrease the angle (θ), sin(θ) decreases, and the downward force becomes weaker.
- If the plane is horizontal (θ = 0°), the downward force is zero (mg sin(0°) = 0).
- If the plane is vertical (θ = 90°), the downward force equals the object's full weight (mg sin(90°) = mg).
5. Is the downward force (mg sin θ) the only force causing an object to accelerate down an incline?
No, not always. The force mg sin(θ) is the component of gravity pulling the object down the slope. However, the net force that determines acceleration also depends on any opposing forces, primarily friction. If friction (f) is present, the net force is F_net = mg sin(θ) - f. Therefore, mg sin(θ) is only the net force if the inclined plane is perfectly smooth and frictionless.
6. What is an example of calculating downward force on an inclined plane in real life?
A classic real-world example is analysing the motion of a skier or a snowboarder on a hill. To understand their acceleration and control their speed, engineers and athletes must consider the downward force of gravity (mg sin(θ)) pulling them down the slope and the opposing forces of friction from the snow and air resistance. The steepness of the slope (θ) is the most critical factor in determining this downward driving force.
7. Why is the component of gravity perpendicular to the plane (mg cos θ) important?
Although the mg cos(θ) component does not cause the object to slide, it is critically important for two reasons. First, it determines the magnitude of the normal force (N = mg cos(θ)), which is the force the surface exerts back on the object. Second, this normal force is then used to calculate the force of friction (f = μN = μmg cos(θ)), where μ is the coefficient of friction. Therefore, the perpendicular component indirectly affects the net acceleration of the object on any surface that isn't perfectly smooth.
