Newton's Second Law of Motion Worksheet
Newton's Second Law of Motion Worksheet
Learning Objectives
By the end of this worksheet, you will be able to: - Calculate net force on objects with multiple forces - Understand the relationship between mass, force, and acceleration - Apply Newton's Second Law (F = ma) to solve problems - Identify the proper units for force, mass, and acceleration
Part 1: Net Force Calculations
When multiple forces act on an object, we must find the net force by adding all forces as vectors.
Example: A 5 kg box has three forces acting on it: 10 N to the right, 5 N to the left, and 3 N upward.
Net force in x-direction: $$F_{net(x)} = 10\text{ N} - 5\text{ N} = 5\text{ N}$$ (right)
Net force in y-direction: $$F_{net(y)} = 3\text{ N}$$ (up)
Total net force: $$F_{net} = \sqrt{5^2 + 3^2} = \sqrt{34} \approx 5.83\text{ N}$$
Problems:
Calculate the net force on a car if the following forces are applied:
- 500 N forward
- 200 N backward
- 50 N to the left
A box has four forces acting on it: 15 N east, 10 N west, 8 N south, and 12 N north. Find the net force.
A boat experiences a 400 N force from its motor and a 150 N force from the current flowing in the opposite direction. What is the net force on the boat?
Part 2: Relationship Between Mass and Acceleration
Newton's Second Law states that: $$F = ma$$, which means $$a = \frac{F}{m}$$
This shows that when force is constant: - If mass increases, acceleration decreases - If mass decreases, acceleration increases
The relationship is inversely proportional.
Problems:
If a constant force is applied to a 2 kg object and a 6 kg object: a) Which object will have greater acceleration? b) How many times greater will the acceleration be?
A force of 24 N causes a cart to accelerate at 3 m/s². If the mass of the cart is doubled: a) What will the new acceleration be? b) What additional force would be needed to maintain the original acceleration?
Explain qualitatively what happens to the acceleration of a rocket as it burns fuel and loses mass (assuming the thrust force remains constant).
Part 3: Relationship Between Force and Acceleration
From $$F = ma$$, we can see that when mass is constant: - If force increases, acceleration increases - If force decreases, acceleration decreases
The relationship is directly proportional.
Problems:
A 5 kg object accelerates at 2 m/s² when a force is applied. If the force is tripled: a) What will the new acceleration be? b) Draw a graph showing the relationship between force and acceleration for this object.
A car of mass 1200 kg accelerates from 0 to 20 m/s in 10 seconds. If the mass stays the same but the engine force increases by 25%: a) How much faster will it reach 20 m/s? b) Explain your reasoning.
Part 4: Solving F = ma Problems
To apply Newton's Second Law, identify the two known variables and solve for the third.
Example: A force of 15 N acts on a 3 kg object. What is the acceleration? $$a = \frac{F}{m} = \frac{15\text{ N}}{3\text{ kg}} = 5\text{ m/s}^2$$
Problems:
A 1500 kg car accelerates at 2 m/s². What force is causing this acceleration?
A force of 250 N causes an object to accelerate at 5 m/s². What is the mass of the object?
During a rocket launch, the engines produce a force of 32,000,000 N. If the rocket's mass is 2,000,000 kg, what is the initial acceleration?
Part 5: Units of Measurement
In the SI system: - Force is measured in newtons (N) - Mass is measured in kilograms (kg) - Acceleration is measured in meters per second squared (m/s²)
From $$F = ma$$, we can derive: $$\text{1 newton} = 1\text{ kg} \cdot \text{m/s}^2$$
Problems:
Convert the following: a) 5000 grams to kilograms b) 0.25 km/s² to m/s²
If a force is measured as 250 N and causes an acceleration of 5 m/s², verify that the unit of the calculated mass is indeed kg.
If mass is doubled and acceleration is halved, what happens to the force in terms of both value and units?
Challenge Problem:
- A 70 kg skydiver jumps from a plane. Before opening their parachute, they experience a downward gravitational force of 686 N and an upward air resistance force that increases with velocity. When the skydiver reaches terminal velocity: a) What is the magnitude of the air resistance? b) What is the net force on the skydiver? c) What is the acceleration of the skydiver at this point? d) If the parachute increases air resistance by a factor of 5, what will be the new terminal velocity? (Hint: at terminal velocity $$F_{net} = 0$$)