Newtons 2nd law of motion

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Name: Joshua Hall Date: 6/19/2024 Newton's Second Law of Motion Problems Worksheet Newton's Second Law of Motion , sometimes called the law of force and motion or law of acceleration , states that: An object acted on by an unbalanced force will accelerate in the direction of that force, in direct proportion to the strength of the force, and in inverse proportion to the mass of the object. Newton's second law is best described with a mathematical equation that relates three va riables, force, acceleration and mass, to one another. The equation can be stated in three forms: force = mass • acceleration mass = force acceleration acceleration = force mass In the first set of problems below, you will be given the mass of an object and the acceleration of that object, and then will need to solve for force, using the equation F —— ma. In other words, you will need to multiply the mass times the acceleration to calculate the force. Be sure to convert any mass stated in grams into kilograms, by dividing it by 1000 (moving the decimal place over three places to the left). For example, 1000 grams is equal to 1 kilogram. Be sure to state the proper units in your answer, and state each answer to the nearest tenth of a unit, to match the accuracy of the measurements. 1. An object with a mass of 2.0 kg accelerates 2.0 m/s 2 when an unknown force is applied to it. What is the amount of the force? 4 newtons 2. An object with a mass of 5.0 kg accelerates 8.0 m/s 2 when an unknown force is applied to it. What is the amount of the force? 40 newtons 3. An object with a mass of 1500 g (grams) accelerates 10.0 m/s* when an unknown force is applied to it. What is the amount of the force? 15,000 Newtons. f = m•a

4. An object with a mass of 6.0 kg accelerates 4.0 m/s 2 when an unknown force is applied to it. What is the amount of the force? 24 Newtons 5. An object with a mass of 7.5 kg accelerates 8.3 m/s 2 when an unknown force is applied to it. What is the amount of the force? 62.25 Newtons 6. An object with a mass of 2000 g accelerates 8.3 m/s* when an unknown force is applied to it. What is the amount of the force? 16,600 Newtons In the second set of problems below, you will be given the force applied to an object and the acceleration of that object, and then will need to solve for mass, using the equation m = F/a. In other words, you will need to divide the force by the acceleration to calculate the mass. Show your work in the space provided. Be sure to state the proper units in your answer, and state each answer to the nearest tenth of a unit, to match the accuracy of the measurements. 7. An object accelerates 3.0 m/s 2 when a force of 6.0 newtons is applied to it. What is the mass of the object? 2.0 kg 8. An object accelerates 12.0 m/s* when a force of 6.0 newtons is applied to it. What is the mass of the object? 0.5 kg 9. An object accelerates 5.0 m/s 2 when a force of 20.0 newtons is applied to it. What is the mass of the object? 4.0 kg 10. An object accelerates 2.0 m/s 2 when a force of 12.0 newtons is applied to it. What is the mass of the object? 6.0 kg 11. An object accelerates 7.2 m/s 2 when a force of 4.0 newtons is applied to it. What is the mass of the object? 0.55 kg 12. An object accelerates 16.3 m/s* when a force of 4.6 newtons is applied to it. What is the mass of the object? 0.28 kg rounds to 0.3 kg In the third set of problems below, you will be given the force applied to an object and the mass of that object, and then will need to solve for acceleration, using the equation a = F/m. In other words, you will need to divide the force by the mass to calculate the acceleration. Be sure to convert any mass stated in grams into kilograms, by dividing it by 1000 (moving the decimal place over three places to the left). For example, 1000 grams is equal to 1 kilogram. Show your work in the space provided. Be sure to state the proper units in your answer, and state each answer to the nearest tenth of a unit, to match the accuracy of the measurements.

3 13. An object with a mass of 2.0 kg has a force of 4.0 newtons applied to it. What is the resulting acceleration of the object? 2 m/s^2 14. An object with a mass of 5.0 kg has a force of 20.0 newtons applied to it. What is the resulting acceleration of the object? 4 m/s 15. An object with a mass of 20.0 kg has a force of 5.0 newtons applied to it. What is the resulting acceleration of the object? 0.25 m/s^2 16. An object with a mass of 3.0 kg has a force of 9.0 newtons applied to it. What is the resulting acceleration of the object? 3 m/s^2 17. An object with a mass of 2300 g has a force of 6.2 newtons applied to it. What is the resulting acceleration of the object? 0.0027 m/s^2 18. An object with a mass of 3.2 kg has a force of 7.3 newtons applied to it. What is the resulting acceleration of the object? 2.3 m/s^2 In the following problems, solve for the missing variable, using the two variables provided. 19. An object accelerates 8.2 m/s 2 when a force of 20.1 newtons is applied to it. What is the mass of the object? 2.5 kg 20. An object with a mass of 6.3 kg has a force of 7.1 newtons applied to it. What is the resulting acceleration of the object? 1.1 m/s^2 21. An object with a mass of 6.5 kg accelerates 12.3 m/s* when an unknown force is applied to it. What is the amount of the force? 80 N

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4 15 N 15 N Newton’s Second Law of Motion Name Joshua Hall Part 1: Newton’s Second Law and Net Force Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the net force on an object and inversely proportional to the mass of the object. We can write this in the form of an equation: a  F net , m where a is the acceleration of the object, F net is the net force acting on it, and m is the object’s mass. The following diagrams show the magnitude and direction of several forces acting on some boxes with masses of 5 kg. The resulting net force and acceleration of each box is calculated using Newton’s Second Law. 10 N 15 N 10 N net force = 10 N to the right acceleration = 10 N/5 kg = 2 m/s 2 to the right net force = 5 N to the left acceleration = 5 N/5 kg = 1 m/s 2 to the left net force = 0 N acceleration = 0 m/s 2 Critical Thinking Questions, Part 1 1. Both net force and acceleration have magnitude and direction. How do the directions of the net force and acceleration compare? The direction of the net force and acceleration are the same.

10 kg 5 N 5 N 20 kg 5 2. The following diagrams show the magnitude and direction of several forces acting on some boxes with different masses. For each one, find the magnitude (with the correct units) and direction (up, down, left, or right) of both the net force and acceleration. a. net force: 0 N magnitude = 0 m/s^2 acceleration: 0 m/s^2 magnitude = 0 m/s^2 direction = Balanced direction = Balanced b. 8 N 20 N net force: 12 Newtons magnitude = N/A acceleration: 1.2 m/s^2 magnitude = N/A direction = Right direction = Right c. 8 N 20 N net force: 28 N magnitude = 0 12 N 12 N acceleration: 70 m/s^2 magnitude = 0 direction = Left direction = N/A 7 N 15 N d. net force: 0 N 2 N 5 N acceleration: 0 m/s^2 22 N magnitude = 0.15 m/s^2 magnitude = 0.15 m/s^2 direction = Down direction = Down 20 kg 0.4 kg

6 Part 2: A Kinematics Reminder Recall that the velocity of an object is how fast it is moving and the direction it moves in. Acceleration is the rate of change of velocity. Therefore, if speed or direction changes (either one is considered a change in velocity), the object is accelerating. Critical Thinking Questions, Part 2 3. Is it possible to say for certain that any of the boxes in question 3 are at rest? Justify your answer. No, it’s not possible any boxes in question 3 are at rest because for the objects that have 0 N force, the box could still be moving at a constant speed in any direction (due to lack of information about the forces going upwards or downwards or starting velocity of the box). Were the boxes do not to have a 0 Newton of force applied, they would be moving in the direction of that force. 4. Which of the boxes in question 3 could be moving with a constant velocity? Justify your answer. Case A is the only one that could be moving with a constant velocity since 5 Newtons to the right – 5 Newtons to the left = 0 Newtons or balance. We do not have information regarding the upward or downward force acting upon the box, it is assumed that it is in constant motion. Since acceleration is not equal to zero in B, C, or D, we can’t justify that it has a constant velocity. 5. Is it possible for the box in question 3b to be moving to the right? If so, is the box’s speed increasing, decreasing, or staying the same? If not, explain why not. Yes, the box is moving towards the right since 20 Newtons to the right – 8 Newtons to the left = 12 Newtons to the right. If the object = 10 kg, to calculate acceleration would be 12 Newtons/10 kg = 1.2 meters per second. Which means if the force is increasing towards the right and already acting towards the right, it will continue to increase towards the right. 6. Is it possible for the box in question 3c to be moving to the right? If so, is the box’s speed increasing, decreasing, or staying the same? If not, explain why not. Yes, it is a possibility that the box could be moving towards the right if the speed is decreasing since the box is already moving towards the left. 7. Suppose the box in question 3d is moving to the right. a. Will the speed of the box increase, decrease, or remain the same?

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7 Remain the same since the next force acting upon the box is zero from left to right. b. Will the direction of motion of the box change? No, since the box was already moving at a net force of zero from left to right, in which the direction will pull downwards as a result of the net force being 3 Newtons down.

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