A student wanted to investigate changing the mass of a cart that you can push. The student pushed both carts with a force of 200 Newtons. If one cart has a mass of 100kg and the other cart a mass of 50kg, what results would the student expect to see as far as how fast each cart moved in comparison with one another?
Type Answer HERE:
The student would expect to see the cart with a mass of 50kg move faster than the cart with a mass of 100kg.
To determine how fast each cart will move in comparison to one another, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
Let's calculate the acceleration of each cart using the formula:
Acceleration = Net Force / Mass
For the cart with a mass of 100kg:
Acceleration = 200 N / 100 kg = 2 m/s²
For the cart with a mass of 50kg:
Acceleration = 200 N / 50 kg = 4 m/s²
Based on these calculations, the student would expect the cart with a mass of 50kg to move faster than the cart with a mass of 100kg. Specifically, the cart with a mass of 50kg will have an acceleration of 4 m/s², while the cart with a mass of 100kg will have an acceleration of 2 m/s². Therefore, the cart with a mass of 50kg will move faster than the cart with a mass of 100kg.
To determine how the mass of the carts affects their speed, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The equation for this is:
F = ma
Where F is the applied force, m is the mass of the object, and a is the acceleration.
In this case, the student is applying a force of 200 Newtons to both carts. Since the force is the same, we can set up the following equation:
F = ma
For the first cart with a mass of 100kg:
200 = 100 * a1
Simplifying, we get:
a1 = 2 m/s²
For the second cart with a mass of 50kg:
200 = 50 * a2
Simplifying, we get:
a2 = 4 m/s²
From these calculations, we can see that the cart with a mass of 50kg will have a higher acceleration than the cart with a mass of 100kg. This means that the cart with the smaller mass will move faster than the cart with the larger mass.