Question

1. a cruise ship and a small cube of ice float next to one another in the ocean. when you press on the cube of ice it quickly moves away from you. when you press on the cruise ship with the same force almost nothing happens. which of newtons laws explains this, and how?
2. a subway passenger is standing inside the subway as it moves to the right. a passenger has dropped motor oil inside the subway car making the floor very slick. the subway car slows down abruptly and you fall forward to the right. which of newtons laws explains why you fell?
3. a bird pushes down on the air with its wings as it flies through the air. the air pushes back on the bird helping to keep it aloft. which of newtons laws explains this?
4. an object with a mass of 5.0 kg accelerates 8.0 m/s² when an unknown net force is applied to it. what must be the magnitude of the net force? show your work.
5. an object of unknown mass has a 100 newton net force applied to it and accelerates at 0.5 m/s². what must be the mass of the object? show your work.
6. an object has a mass of 450 kg and has a net force of 1,000 newtons applied to it. what is the magnitude of the objects acceleration? show your work.
7. a 10 kg ball is tied between two horizontal ropes. the ball is pulled to the left by a tension force of 40 newtons and pulled to the right by a force of unknown magnitude. the ball accelerates to the right with a constant acceleration of 0.5 m/s². ignore forces in the y direction.

i. calculate the magnitude and direction of the net force on the ball (remember, net force means total force)
ii. calculate the magnitude of the tension force pulling the ball to the right

Explanation:

Step1: Apply Newton's second law

Newton's second law is \(F_{net}=ma\). Given \(m = 10\space kg\) and \(a=0.5\space m/s^{2}\)

$$F_{net}=ma$$

$$F_{net}=10\times0.5$$

$$F_{net} = 5\space N$$

Since the acceleration is to the right, the net force is to the right.

Step2: Set up force equation

Let \(F_{right}\) be the force pulling to the right and \(F_{left}=40\space N\) (pulling to the left). Using \(F_{net}=F_{right}-F_{left}\)

$$F_{right}=F_{net}+F_{left}$$

Substitute \(F_{net} = 5\space N\) and \(F_{left}=40\space N\)

$$F_{right}=5 + 40$$

$$F_{right}=45\space N$$

Answer:

i. The magnitude of the net force is \(5\space N\) and the direction is to the right.
ii. The magnitude of the tension force pulling the ball to the right is \(45\space N\)