A 1.5 kg otter starts from rest at the top of a
muddy incline 80.2 cm long and slides down
to the bottom in 0.40 s.
What net external force acts on the otter
along the incline?
Answer in units of N
To find the net external force acting on the otter along the incline, we can use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object times its acceleration.
First, we need to find the acceleration of the otter. We can use the kinematic equation:
\(s = ut + \frac{1}{2}at^2\)
where \(s\) is the distance traveled, \(u\) is the initial velocity (which is zero in this case since the otter starts from rest), \(a\) is the acceleration, and \(t\) is the time.
In this case, the distance \(s\) is the length of the incline, which is 80.2 cm (0.802 m), and the time \(t\) is given as 0.40 s. Plugging these values into the equation, we can solve for \(a\):
\(0.802 = 0 + \frac{1}{2}a(0.40)^2\)
Simplifying the equation:
\(0.802 = 0.08a\)
Dividing both sides by 0.08:
\(a = \frac{0.802}{0.08} = 10.025 \, \text{m/s}^2\)
Now that we have the acceleration, we can find the net external force by multiplying the mass of the otter (1.5 kg) by the acceleration:
\(F_{\text{net}} = ma = 1.5 \times 10.025 \, \text{N}\)
Thus, the net external force acting on the otter along the incline is 15.038 N.