# What net external force acts on the otter along the incline? Answer in units of N.A 1.7 kg otter starts from rest at the top of a muddy incline 93 cm long and slides down to the bottom in 0.40 s.

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### 2 Answers

The ball starts with a zero velocity and reaches bottom along a 93 cm innclined path.Let a be the net acceleration.

Then ut+(1/2)at^2= S,displacement, where u is the initial velocity which is 0. The net acceleration, a is to be found out t=0.4s and displacement S=93 cm

0*.4+(1/2)a(.4)^2=93 or

0+(1/2)a*0.16=93

a=93*2/0.16= 1162.5cm/s^2.

Therefore the net force acting =mass*acceleration

=1.8kg*11.625m/s^2

=20.925 N is the net force on the object to traverse 93 cm in 0.4 seconds.

The otter basically experiences a downward force due to gravity. This force has two components one acting the incline, and other at right angles to incline. As the otter tries to slide down the incline under the influence of force parallel to incline it is resisted by force of friction between otter and incline. However in this case the force trying to slide the otter down is more than the frictional force. Thus the otter slides down the incline with a net force equal to component of gravitational force parallel to incline less the frictional force.

Let us say this force = F, and because of this the the otter slides down with acceleration of "a". In this process it covers a distance "s" equal to 93 cm (0.93 m) in time "t" 0.4.

in this situation the acceleration "a" of the otter is given by the equation:

a = 2s/(t^2) = 2*0.93/[(0.4)^2] = 11.625 m/s^2

As it can be seen this acceleration is more than the acceleration due to gravity. This means that some external force in addition to gravitational force is applied to the otter.

To know the exact external force we will need to know the angle of incline, as well as coefficient of friction, so that we can calculate the gravitational force along the incline and the frictional force along opposite to it. In absence of this let us assume that there is no frictional force and the full force of gravity is made to act along the incline by some device. Then the

External force = (Total acceleration - acceleration due to gravity)*(Mass of otter)

= (11.625 - 9.8)*1.7 = 3.1025 N