calculate the horizontal force that must be applied to a 1-kg puck to make it accelerate on a horizontal friction-free air table with the same acceleration it would have if it were dropped and fell freely?
F = M a
Since (horizontal) acceleration a = g, you need a force equal to the weight,
F = M g = 9.8 Newtons
Why did the puck break up with its significant other?
Because it wanted to experience some "free fall" in love!
Now, back to your question. If we assume that the acceleration due to gravity is approximately 9.8 m/s² and we want the puck to have the same acceleration horizontally, we'll use Newton's second law: F = m * a.
The mass of the puck is given as 1 kg, and since we want the same acceleration horizontally as in free fall (9.8 m/s²), the force required would be:
F = 1 kg * 9.8 m/s² = 9.8 N
So, you must apply a horizontal force of 9.8 Newtons to the 1-kg puck on the friction-free air table to make it accelerate horizontally at the same rate as if it were freely falling.
To calculate the horizontal force required to make the 1-kg puck accelerate on a friction-free air table, we need to use Newton's second law of motion. The formula for Newton's second law is:
F = m * a
Where:
F is the force (in Newtons),
m is the mass of the object (in kilograms),
a is the acceleration (in meters per second squared).
In this case, the mass of the puck is given as 1 kg. To find the acceleration that the puck would have if it were dropped and fell freely, we can use the acceleration due to gravity, which is approximately 9.8 m/s².
Therefore, the horizontal force required to make the puck accelerate with the same acceleration as free fall would be:
F = 1 kg * 9.8 m/s²
F = 9.8 N
So, the horizontal force that must be applied to the 1-kg puck is 9.8 Newtons.
To calculate the horizontal force required to make the puck accelerate on a friction-free air table, we need to understand the concept of free fall acceleration.
In free fall, an object falls under the influence of gravity without any other forces acting on it. Gravity causes an object to accelerate at approximately 9.8 m/s² near the Earth's surface. This value is commonly represented as "g" and can vary slightly depending on location.
Now, let's solve the problem step by step:
1. Determine the acceleration of the puck when dropped and falling freely:
Since the puck is in free fall, its acceleration will be equal to the acceleration due to gravity, which is approximately 9.8 m/s².
2. Recognize that this same acceleration needs to be achieved on the friction-free air table:
To make the puck accelerate on the air table with the same acceleration as free fall, we need to apply an external force equal to the force of gravity acting on the puck.
3. Calculate the force of gravity acting on the puck:
The force of gravity can be calculated using the equation:
Force of gravity = mass × acceleration due to gravity
Given that the mass of the puck is 1 kg and the acceleration due to gravity is 9.8 m/s², we have:
Force of gravity = 1 kg × 9.8 m/s² = 9.8 N
Therefore, a horizontal force of 9.8 Newtons must be applied to the 1-kg puck to make it accelerate on a friction-free air table with the same acceleration it would have if it were dropped and fell freely.