You are participating in the Iditarod, and your sled dogs are pulling you across a frozen lake with a force of 1200N while a 300N wind is blowing at you at 135 degree from your direction of travel. What is the net force, and will your kinetic energy increase or decrease?
To find the net force, we need to consider both the force applied by the sled dogs and the force exerted by the wind. Since the force applied by the sled dogs is in the direction of travel and the force exerted by the wind is in the opposite direction, we can subtract the two forces.
1. First, let's break down the forces into their horizontal components. The force applied by the sled dogs can be represented as 1200N in the forward direction while the force exerted by the wind can be broken down into its horizontal component, which can be calculated using the cosine function:
Horizontal component of wind force = wind force * cos(angle)
= 300N * cos(135°)
2. Now that we have the horizontal components of both forces, we can find the net horizontal force by subtracting the horizontal component of the wind force from the force applied by the sled dogs:
Net horizontal force = force applied by sled dogs - horizontal component of wind force
3. Finally, we can determine the net force using the Pythagorean theorem since the net force is the resultant of both the horizontal and vertical components:
Net force = sqrt((Net horizontal force)^2 + (Vertical component of wind force)^2)
After finding the net force, we can determine if your kinetic energy will increase or decrease. Kinetic energy is directly proportional to the square of the velocity, which depends on the net force acting on an object. If the net force is greater than zero, your kinetic energy will increase. If the net force is less than zero, your kinetic energy will decrease. And if the net force is equal to zero, your kinetic energy will remain constant.
So, to summarize:
1. Calculate the horizontal component of the wind force.
2. Calculate the net horizontal force.
3. Calculate the vertical component of the wind force.
4. Calculate the net force using the Pythagorean theorem.
5. Determine whether your kinetic energy will increase, decrease, or remain constant based on the net force.
Fn = 1200 + 300[135o] = 1200 + 300*Cos135+i300*sin135 = 989 + 212i = 1011N.
KE decreased.