Question

When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 2 kg, the acceleration of the object is 39 /ms2. When the same force acts upon another object, its acceleration is 6 /ms2. What is the mass of this object?

Answer 1

According to the problem, the acceleration of an object varies inversely with its mass when a constant force is applied. This can be expressed as:

a = k/m

where a is the acceleration, m is the mass, and k is the constant of proportionality.

We can use this equation to solve for k:

k = am

For the first object with mass 2 kg and acceleration 39 m/s^2:

k = am = (39 m/s^2)(2 kg) = 78 N

Now we can use this value of k to solve for the mass of the second object, which has an acceleration of 6 m/s^2:

k = am = (6 m/s^2)(m) = 6m

78 N = 6m

m = 78 N / 6 = 13 kg

Therefore, the mass of the second object is 13 kg.