Question

Thinking about the winter we missed out on this year. Calvin and his tiger go sledding down a snowy hill. There is friction between the snow and the sled, and there is air resistance. Looking at the entire time that they spend on the hill (from when they start from rest at the top of the hill until they reach the bottom moving fast), indicate whether each of the following quantities is positive, negative, or zero, by writing either +, -, or 0 for the questions below. We take Calvin, the tiger, and the sled as our system.

The work done by the frictional force that the snow exerts on the system is ?

Answer 1

As they are sledding down the hill, friction acts in the opposite direction to the motion, that is up the hill.

Direction of displacement of the system is down the hill.

We have, work done = dot product of force and displacement

that is,

where F is the magnitude of force and S is the displacement and   is the angle between these two vectors.

Here, let F be the frictional force and S be the displacement of the system down the hill.

therefore   = 1800   ....(as they are in opposite directions)

Therefore, work done is

Magnitudes of force and displacement are positive quantities. Therefore the negative sign shows that the work done by the frictional force is negative.