A force is applied to a 2.7 kg mass and produces 2.9 m/s

2
acceleration.
What acceleration would be produced by
the same force applied to a 14.9 kg mass?
Answer in units of m/s
2

.52550

To find the acceleration produced by the same force applied to a 14.9 kg mass, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

Given:
Mass of the first object (m1) = 2.7 kg
Acceleration of the first object (a1) = 2.9 m/s^2
Mass of the second object (m2) = 14.9 kg

Using Newton's second law, we can set up the following equation:

F = m * a

For the first object: F = m1 * a1

For the second object: F = m2 * a2 (we need to find a2)

Since the force applied is the same in both cases, we can equate the two equations:

m1 * a1 = m2 * a2

Plugging in the given values:

2.7 kg * 2.9 m/s^2 = 14.9 kg * a2

Solving for a2:

a2 = (2.7 kg * 2.9 m/s^2) / 14.9 kg

a2 ≈ 0.527 m/s^2

Therefore, the acceleration produced by the same force applied to a 14.9 kg mass would be approximately 0.527 m/s^2.

To find the acceleration produced by the same force applied to a different mass, 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.

The formula for Newton's second law is:

a = F/m

where:
a = acceleration
F = force applied
m = mass of the object

Given that the force applied is the same, we can set up a proportion to solve for the acceleration:

a₁ / m₁ = a₂ / m₂

where:
a₁ = acceleration for the first mass (2.7 kg)
m₁ = mass for the first mass (2.7 kg)
a₂ = acceleration for the second mass (to be determined)
m₂ = mass for the second mass (14.9 kg)

Substituting the given values:

a₁ / 2.7 kg = a₂ / 14.9 kg

Now, we can solve for a₂ by rearranging the equation:

a₂ = (a₁ / 2.7 kg) * 14.9 kg

Plugging in the values:
a₂ = (2.9 m/s²) * 14.9 kg

Calculating the result:
a₂ = 43.21 m/s²

Therefore, the acceleration produced by the same force applied to a 14.9 kg mass would be 43.21 m/s².

f = m a __ acceleration is inversely proportional to the mass

a = 2.9 m/s^2 * (2.7 / 14.9)