A force is applied to a 1.3 kg mass and produces 4.2 m/s
2
acceleration.
What acceleration would be produced by
the same force applied to a 7.5 kg mass?
Answer in units of m/s
Just apply the tried-and-true F=ma formula.
F = 1.3 * 4.2 = 5.46N
5.46 = 7.5a, so a = 5.46/7.5 = 0.728 m/s^2
To find the acceleration produced by the same force applied to a 7.5 kg mass, we can use Newton's second law of motion:
F = m * a
Where:
F is the force
m is the mass
a is the acceleration
So, using the given values:
Force = ?
Mass (m1) = 1.3 kg
Acceleration (a1) = 4.2 m/s^2
We can rearrange the formula to find the force:
F = m1 * a1
F = 1.3 kg * 4.2 m/s^2
F = 5.46 kg*m/s^2
Now, we can use the force (F) and the mass (m2 = 7.5 kg) to find the acceleration (a2):
F = m2 * a2
5.46 kg*m/s^2 = 7.5 kg * a2
a2 = 5.46 kg*m/s^2 / 7.5 kg
a2 ≈ 0.728 m/s^2
So, the acceleration produced by the same force applied to a 7.5 kg mass is approximately 0.728 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 force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
Where:
F is the force (unknown)
m is the mass of the object (7.5 kg)
a is the acceleration (unknown)
We can rearrange the equation to solve for acceleration:
a = F / m
Given that the force applied to the 1.3 kg mass produces an acceleration of 4.2 m/s^2, we can plug in the known values:
4.2 m/s^2 = F / 1.3 kg
Now, we can solve for the force:
F = 4.2 m/s^2 * 1.3 kg
F ≈ 5.46 N
Finally, we can substitute the calculated force (5.46 N) and the mass of the new object (7.5 kg) into the formula to find the acceleration:
a = F / m
a = 5.46 N / 7.5 kg
Calculating this:
a ≈ 0.73 m/s^2
Therefore, the acceleration produced by the same force applied to a 7.5 kg mass would be approximately 0.73 m/s^2.