3. Two kids are fighting over a toy. Karen pulls the toy to her side with a force of 10 N, while Susan pulls it to her side with a force of 12 N. If the toy weighs 360 g, how much acceleration was imparted on the toy? To which side will it accelerate?4. A 145-g baseball was hit by a bat. If the ball was hit by a 6-N force, how much acceleration
did the ball gain?5. A piece of rope can withstand a tension of 1500 N. If it is used to pull an object to give it an
acceleration of 1.75 m/s², what is the maximum mass of the object that it can pull without
snapping?6. The moon causes an object near its surface to fall with an acceleration of 1.7 m/s². Let's say a steel ball was hung from a spring balance in the moon. The spring balance was read and it indicated that the steel ball was being pulled by the moon with a force of 2.55 N. How much does the steel ball weigh?
To solve these problems, we will be using Newton's second law, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
For question 3:
Given:
- Karen's force: 10 N
- Susan's force: 12 N
- Toy's weight: 360 g
First, we need to convert the weight of the toy from grams to kilograms:
Weight = mass × acceleration due to gravity
Weight = (360 g) × (1 kg/1000 g) ≈ 0.36 kg
To find the acceleration of the toy, we need to calculate the net force acting on it. This can be found by subtracting Susan's force from Karen's force:
Net force = Susan's force - Karen's force
Net force = 12 N - 10 N = 2 N
Now, we can find the acceleration:
Net force = mass × acceleration
2 N = (0.36 kg) × acceleration
Solving for acceleration:
acceleration = 2 N / 0.36 kg ≈ 5.56 m/s²
Since the net force is positive (Susan's force is greater), the toy will accelerate towards Susan's side.
For question 4:
Given:
- Force: 6 N
- Baseball's mass: 145 g
First, we need to convert the mass of the baseball from grams to kilograms:
Mass = 145 g × (1 kg/1000 g) ≈ 0.145 kg
Now, we can find the acceleration:
Force = mass × acceleration
6 N = (0.145 kg) × acceleration
Solving for acceleration:
acceleration = 6 N / 0.145 kg ≈ 41.38 m/s²
The ball gained an acceleration of approximately 41.38 m/s².
For question 5:
Given:
- Maximum tension: 1500 N
- Acceleration: 1.75 m/s²
We will use the formula:
Tension = mass × acceleration
Solving for mass:
mass = Tension / acceleration
mass = 1500 N / 1.75 m/s² ≈ 857.14 kg
The maximum mass of the object that the rope can pull without snapping is approximately 857.14 kg.
For question 6:
Given:
- Acceleration due to moon's gravity: 1.7 m/s²
- Force measured by spring balance: 2.55 N
To find the weight of the steel ball, we can use the equation:
Weight = mass × acceleration due to gravity
First, we need to find the mass of the steel ball. We know that the force measured by the spring balance is equal to the weight of the object:
Force = Weight = mass × acceleration due to gravity
2.55 N = mass × 1.7 m/s²
Solving for mass:
mass = 2.55 N / 1.7 m/s² ≈ 1.5 kg
The steel ball weighs approximately 1.5 kg.