# Numericals on Force and Laws of Motion for Class 9

Home » CBSE Class 9 Science » Extra Questions for Class 9 Science » Numericals on Force and Laws of Motion for Class 9

## Numericals on Force and Laws of Motion for Class 9

Here you will find numericals on force and laws of motion for class 9.

Problem:

Find the force acting on a rocket and its acceleration if its velocity is 600 m s–1 at t = 60 s and 1000 ms–1 at t = 80s, presuming its mass remains unchanged during this time interval and its mass is 1.67 × 107 kg. The total weight of the rocket at t = 80 seconds is 1.6 × 107 kg. Calculate the upward force acting on the rocket at this time caused by the burning of fuel.

Solution:

(i) Calculate the acceleration ($$a$$) and force ($$F$$) at $$t=60$$ seconds: \begin{aligned} a &= \frac{v-u}{t} = \frac{1000 \mathrm{~m/s} – 600 \mathrm{~m/s}}{80 \mathrm{~s} – 60 \mathrm{~s}} = \frac{400 \mathrm{~m/s}}{20 \mathrm{~s}} = 20 \mathrm{~m/s^2} \\ F &= m \cdot a = 1.67 \times 10^7 \mathrm{~kg} \times 20 \mathrm{~m/s^2} = 3.34 \times 10^8 \mathrm{~Newton} \end{aligned} (ii) Calculate the force ($$F$$) at $$t=80$$ seconds using the new total weight: $F = m \cdot a = 1.6 \times 10^7 \mathrm{~kg} \times 20 \mathrm{~m/s^2} = 3.2 \times 10^8 \mathrm{~Newton} = 320 \mathrm{~MN}$

Problem:

A body of 10 kg initially at rest is subjected to force of 20N. Calculate the kinetic energy acquired by the body at the end of 10 seconds.

Solution:

Given: $$m = 10 \mathrm{~kg}$$, $$u = 0$$, $$F = 20 \mathrm{~N}$$, $$t = 10 \mathrm{~s}$$ First, calculate the acceleration ($$a$$) using Newton’s second law: $F = m \cdot a \Rightarrow a = \frac{F}{m} = \frac{20 \mathrm{~N}}{10 \mathrm{~kg}} = 2 \mathrm{~m/s^2}$ Next, calculate the final velocity ($$v$$) using the equation of motion: $a = \frac{v – u}{t} \Rightarrow \frac{v – 0}{10 \mathrm{~s}} = 2 \mathrm{~m/s^2} \Rightarrow v = 20 \mathrm{~m/s}$ Finally, calculate the kinetic energy ($$KE$$) using the formula for kinetic energy: $KE = \frac{1}{2} m v^2 = \frac{1}{2} \cdot 10 \mathrm{~kg} \cdot (20 \mathrm{~m/s})^2 = 2000 \mathrm{~J} = 2 \mathrm{~kJ}$ So, the kinetic energy acquired by the body at the end of 10 seconds is $$2 \mathrm{~kJ}$$.

Problem:

A truck starts from the rest and rolls down a hill with constant acceleration. It travels 200 m in 20 s. Find its acceleration. Find the force acting on it, if its mass is 5 metric tonnes. (1 metric tonne = 1000 kg)

Solution:

Given: $$u = 0$$, $$t = 20 \mathrm{~s}$$, $$s = 20 \mathrm{~m}$$, $$a = ?$$, $$\mathrm{F} = ?$$, $$m = 5000 \mathrm{~kg}$$ Using the equation of motion: $s = ut + \frac{1}{2}at^2$ Substituting the given values: $20 \mathrm{~m} = 0 + \frac{1}{2} \cdot a \cdot (20 \mathrm{~s})^2$ Solving for acceleration $$a$$: $a = \frac{400}{400} = 1 \mathrm{~m/s^2}$ Now, using Newton’s second law ($$F = ma$$) to find the force ($$\mathrm{F}$$): $\mathrm{F} = m \cdot a = 5000 \mathrm{~kg} \cdot 1 \mathrm{~m/s^2} = 5000 \mathrm{~Newton}$ So, the acceleration ($$a$$) is $$1 \mathrm{~m/s^2}$$ and the force ($$\mathrm{F}$$) is $$5000 \mathrm{~Newton}$$.

Problem:

A bullet of mass 10 g is horizontally fired with a velocity of 100 m s–1 from pistol of mass 1 kg. What is the recoil velocity of the pistol?

Solution:

Given: $$m = 10 \mathrm{~g} = \frac{10}{1000} \mathrm{~kg}$$, $$v = 100 \mathrm{~m/s}$$, $$\mathrm{M} = 1 \mathrm{~kg}$$, $$\mathrm{V} = ?$$
Using the formula for the velocity of the gun in the opposite direction to the bullet: $\mathrm{V} = -\frac{m v}{\mathrm{M}} = -\frac{\frac{10}{1000} \mathrm{~kg} \times 100 \mathrm{~m/s}}{1 \mathrm{~kg}}$ Solving for $$\mathrm{V}$$: $\mathrm{V} = -1 \mathrm{~m/s}$ So, the velocity of the gun is $$-1 \mathrm{~m/s}$$ in the opposite direction to the bullet being fired.

## Force and Laws of Motion Class 9 Important Formula

1. $$1 \, \text{Newton} = 1 \, \text{kg} \, \text{m/s}^{-2}$$; newton ($$\text{N}$$) is the SI unit of force.
2. $$\vec{p} = \overrightarrow{m \mathbf{v}}$$, where $$\vec{p}$$ is momentum, $$m$$ is mass, and $$\mathbf{v}$$ is velocity.
3. $$\vec{F} = \frac{\overrightarrow{p_f} – \overrightarrow{p_i}}{t} = \frac{m \mathbf{v} – m \mathbf{u}}{t} = \frac{m(\mathbf{v} – \mathbf{u})}{t} = m \mathbf{a}$$, where $$a$$ = acceleration. $$\frac{v-u}{t} = a]$$
4. $$\overrightarrow{\mathbf{F}} = m \mathbf{a}$$ Impulse $$= \text{force} \times \text{time} = \text{change in momentum}$$
5. $$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$$ : Law of conservation of momentum.
6. Recoil of gun: $$\mathbf{V} = \frac{-m \mathbf{v}}{\mathbf{M}}$$, where $$m$$ is the mass of the bullet, $$M$$ is the mass of the gun, $$\mathbf{V}$$ is the velocity of the gun, and $$\mathbf{v}$$ is the velocity of the bullet.
7. $$\frac{\text{Rocket propulsion}}{\text{Velocity of rocket}} = V = \frac{-mV}{M}$$, where $$m$$ is the mass of burnt fuel, $$v$$ is the velocity of burnt fuel, and $$M$$ is the mass of the rocket at any instant.

## Why are Physics Numericals Important for Class 9 Students?

1. Application of Concepts: Physics numericals allow students to apply the theoretical concepts they learn in class to real-world situations. This practical application enhances their understanding of the subject.
2. Problem-Solving Skills: Numerical problems require critical thinking and problem-solving skills. Students learn to analyze information, identify relevant formulas, and calculate solutions, skills that are valuable in many aspects of life.
3. Enhanced Understanding: By solving numerical problems, students gain a deeper insight into the underlying principles of physics. It’s one thing to memorize formulas, but it’s another to comprehend how they are derived and applied.
4. Preparation for Higher Classes: A strong foundation in physics at the Class 9 level prepares students for more advanced physics topics in higher classes. It paves the way for success in Class 10 board exams and beyond.

## Tips for Solving Physics Numericals

1. Understand the Concept: Before attempting numericals, ensure you have a clear understanding of the underlying physics concepts. Review your class notes and textbook.
2. Identify Given Data: Carefully read the problem and identify the given data. This is crucial for selecting the appropriate formula.
3. Choose the Right Formula: Select the formula that best fits the problem. Familiarize yourself with the relevant equations for each topic.
4. Units and Conversions: Pay attention to units. Ensure all units are consistent throughout your calculations, and convert them if necessary.
5. Organize Your Work: Show your work step by step. This not only helps you track your progress but also allows for partial credit if you make a mistake.
6. Practice Regularly: Physics numericals improve with practice. The more problems you solve, the more confident and proficient you’ll become.
7. Seek Help When Needed: If you’re stuck on a problem, don’t hesitate to seek help from your teacher, classmates, or online resources.
Announcements

Join our Online JEE Test Series for 499/- Only (Web + App) for 1 Year

Join our Online NEET Test Series for 499/- Only for 1 Year