Question

A standard object defined as having a mass of exactly 8.86 kg is given an acceleration of 2.27 m/s 2 when a certain force is applied to it. A second object of unknown mass acquires an acceleration of 1.0721 m/s 2 when the same force is applied to it. What is the mass of the second object? Answer in units of kg.

Answer 1

To find the unknown mass of the second object, we use the relation F = ma, given that the same force is applied to both objects. We set up a ratio of the masses and accelerations of both objects and solve for the unknown mass, yielding a result of 17.734 kg.

Step-by-step explanation:

To find the mass of the second object, we use Newton's Second Law of Motion, which states that the force F acting on an object is equal to the mass m of the object multiplied by the acceleration a it experiences (F = ma). Since the same force is applied to both objects, we can set up a ratio of the masses and accelerations.

For the first object with mass m1 = 8.86 kg and acceleration a1 = 2.27 m/s2, the force is F = m1 * a1. For the second object with unknown mass m2 and acceleration a2 = 1.0721 m/s2, the force is the same, F = m2 * a2.

Setting the forces equal gives us the equation:
m1 * a1 = m2 * a2
Now we can solve for m2:

m2 = (m1 * a1) / a2
m2 = (8.86 kg * 2.27 m/s2) / 1.0721 m/s2
m2 = 19.0132 kg / 1.0721
m2 = 17.734 kg

The mass of the second object is 17.734 kg.

Answer 2

Mass of second object = 18.76 kg

Step-by-step explanation:

We have force is the product of mass and acceleration,

Force = Mass x Acceleration

F = ma

A standard object defined as having a mass of exactly 8.86 kg is given an acceleration of 2.27 m/s² when a certain force is applied to it.

Force applied, F = 8.86 x 2.27 = 20.11 N

A second object of unknown mass acquires an acceleration of 1.0721 m/s² when the same force is applied to it.

Force = Mass x Acceleration

20.11 = Mass x 1.0721

Mass = 18.76 kg

Mass of second object = 18.76 kg