3.3 Using Newton's 2nd Law

3.3 Using Newton's Second Law

Mass and Acceleration

• ​Recall our previous discussion: when pushing a shopping cart, what happens?

• If you apply a constant force to the cart, what happens as more items are added in?

• The cart moves faster when it is empty than when it is loaded with groceries, so the cart's acceleration is inversely proportional to its mass.

• This relationship can be written mathematically as  a ∝ 1/m

• Where ∝ means “proportional to.”

Force and Acceleration

• What happens when I push the cart with a greater force?

• What if your friend tried to pull the cart in the opposite direction you are pushing it in?

• The acceleration of the cart changes as the net force acting on it changes.

• If your push on the cart is greater than the pull of your friend, the cart will move in the direction of your push.

• So the cart's acceleration is directly proportional to and in the direction of the net force acting on the cart.

• This relationship is expressed mathematically as  a ∝ ΣF

Multiple Select

According to Newton's Second Law, the acceleration is directly proportional to the net force acting on it in the direction of the net force, and inversely proportional to its mass. Which of the following show this representation mathematically?

• $$\sum_{ }^{ }\overrightarrow{F}=ma$$

• $$a=\sum_{ }^{ }\frac{\overrightarrow{F}}{m}$$

• $$F=ma$$

• $$\sum_{ }^{ }\overrightarrow{F}=0$$

• $$\sum_{ }^{ }\overrightarrow{F}=\frac{a}{m}$$

Newton's Second Law

• The equation for Newton’s second law of motion can also be broken down into its rectangular components.

• For example, the net force acting on an object in the  ,  , and   directions ca be mathematically written as: ΣF_x = ma_x, ΣF_y = ma_y, and ΣF_z = ma_z 

• A force applied in the direction of the object’s motion accelerates the object, and a force applied in the direction opposite to the object’s motion decelerates it. 

• A force applied at right angles to the object deflects the object, and a force applied in any other direction changes the speed, as well as the direction, of the object. 

Multiple Choice

If Pete pushes a toy car across the floor, which statement is true according to Newton's second law of motion?

• The force applied by Pete is greater than the frictional force between the car and the floor.

• The net force acting on the toy car is zero.

• The toy car is in static equilibrium

• Zero net force is required to make the toy car slow down, that is, decelerate.

Math Response

What is the force required to accelerate a baseball with a mass of 0.145 kilograms and an acceleration of 35.00 m/s²? [Just give the value]

Type answer here

Correct Answer: 5.08

Deg^°

Rad

Multiple Choice

Dave pushes a shopping cart with a constant force of 10.0 N across the floor of a grocery store. The frictional force exerted by the floor is 4.0 N, and the acceleration of the cart is 1.0 m/s². What is the mass of the shopping cart?

• 6.0 kg

• 10.0 kg

• 4.0 kg

• 14.0 kg

Drag and Drop

Sophia pushes a shopping cart of mass 5 kg with a force of 12 N across the floor of a grocery store. The floor exerts a frictional force of 3 N, and her son, Mark, is dragging his feet while holding the cart for a force of 5 N. The net force is ​

Placeholder

N and the acceleration of the cart is​

Placeholder

m/s².

Drag these tiles and drop them in the correct blank above

4

0.8

10

14

7

2.0

2.8

1.4

9

1.8

Math Response

A vehicle of mass 1,000 kg is moving at a speed of 27.5 m/s. The driver slows down to a speed of 17.22 m/s in 15 seconds. Find the force that acts on the vehicle during this time. Assume constant force and no friction. Round your answer to the nearest integer.

Type answer here

Correct Answer: -685

Deg^°

Rad

Draw

An ice hockey player hits a puck of mass 0.15 kilograms with a force of 100 newtons in the horizontal direction. What is the acceleration produced by the force in the horizontal direction? 

Draw a free-body diagram to illustrate this problem. Write down the relevant equation(s) to solve the problem and then solve it.

Open Ended

What does the video say about the application of Newton’s second law of motion in football?

Open Ended

You have an old-style reel lawn mower at home. No engine! You need to cut the grass but also finish in time to watch your favorite TV show. How would you apply Newton’s second law of motion here?

Open Ended

You and your friends are going on a picnic in a very small car. On your way, the car breaks down and you try to push it to get it to move but in vain. You ask your friends to help you and the car starts moving and revs up. How are you and your friends applying Newton’s second law of motion here?