Question

A rock with mass m = 3.60 kg falls from rest in a viscous medium. The rock is acted on by a net constant downward force of F = 15.0 N (a combination of gravity and the buoyant force exerted by the medium) and by a fluid resistance force f=kv, where v is the speed in m/s and k = 2.68 N×s/m.(a) Find the initial acceleration a0 (b) Find the acceleration when the speed is 3.60 m/s.

Answer 1

To find the initial acceleration (a0), use Newton's second law. The acceleration when the speed is 3.60 m/s can be found by considering the net force on the rock.

Step-by-step explanation:

To find the initial acceleration a0, we can use Newton's second law which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, the net force on the rock is given as F = 15.0 N. So, we have:

F = m * a0

Solving for a0, we get:

a0 = F / m

Plugging in the values, we have a0 = 15.0 N / 3.60 kg = 4.17 m/s².

To find the acceleration when the speed is 3.60 m/s, we can rearrange the equation for the fluid resistance force:

f = kv

to:

v = f / k

Plugging in the values, we have v = 3.60 m/s, k = 2.68 N×s/m. Solving for f, we get:

f = k * v = 2.68 N×s/m * 3.60 m/s = 9.65 N

Now, the net force on the rock is the sum of the constant downward force F and the fluid resistance force f. So, we have:

F + f = m * a

Solving for a, we get:

a = (F + f) / m

Plugging in the values, we have a = (15.0 N + 9.65 N) / 3.60 kg = 6.48 m/s².