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?
According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. The formula for acceleration is:
acceleration = force / mass
In this case, both carts are pushed with a force of 200 Newtons. Therefore, using the formula above, we can calculate the acceleration of each cart.
For the cart with a mass of 100kg:
acceleration_cart1 = 200 N / 100 kg = 2 m/s^2
For the cart with a mass of 50kg:
acceleration_cart2 = 200 N / 50 kg = 4 m/s^2
From these calculations, we can see that the cart with a mass of 50kg would experience twice the acceleration compared to the cart with a mass of 100kg. This means that the lighter cart would move faster than the heavier cart when pushed with the same force.
To determine how the speed of the carts would vary with different masses, we need to consider Newton's second law of motion. According to this law, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
The formula for Newton's second law is:
F = m * a
Where:
F = Net force applied to the object
m = Mass of the object
a = Acceleration of the object
In this case, the student applied a constant force of 200 Newtons to both carts. Let's calculate the acceleration of each cart using Newton's second law:
For the cart with a mass of 100 kg:
F = m * a
200 N = (100 kg) * a
Using this equation, we can solve for 'a':
a = 200 N / 100 kg
a = 2 m/s²
For the cart with a mass of 50 kg:
F = m * a
200 N = (50 kg) * a
Again, solving for 'a':
a = 200 N / 50 kg
a = 4 m/s²
Based on these calculations, we can see that the acceleration of the cart with a mass of 50 kg is double that of the cart with a mass of 100 kg. However, since the student applied the same force to both carts, the cart with a mass of 50 kg would experience twice the acceleration compared to the cart with a mass of 100 kg. As a result, the cart with a lower mass would be expected to move faster than the cart with a higher mass.
To determine how fast each cart would 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 force applied and inversely proportional to the mass of the object.
Using this law, we can calculate the acceleration of each cart using the formula:
acceleration = force / mass
For the cart with a mass of 100kg:
acceleration = 200 N / 100 kg
acceleration = 2 m/s^2
For the cart with a mass of 50kg:
acceleration = 200 N / 50 kg
acceleration = 4 m/s^2
Therefore, the student would expect to see the cart with a mass of 50kg move faster than the cart with a mass of 100kg.