# Later on over the break, you decide to go sledding. To get to the top of the hill, you and your...

## Question:

Later on over the break, you decide to go sledding. To get to the top of the hill, you and your sled (total mass of 80 kg, we'll say), are pulled at a constant speed by a tow rope that maintains a constant tension of 340 N. How much thermal energy is produced between the hill and your sled during the ascent of a 30-m-high, 120-m-long slope?

## Energy

Energy is the ability to change the state of the system. For an isolated system, the total energy always remains constant but the form of energy may change at various states.

Given data:

• The mass is: {eq}m = 80\;{\rm{kg}} {/eq}
• The tension force is: {eq}T = 340\;{\rm{N}} {/eq}
• The height of the hill is: {eq}h = 30\;{\rm{m}} {/eq}
• The length of the slope is: {eq}l = 120\;{\rm{m}} {/eq}

Write the expression for the thermal energy produced.

{eq}\begin{align*} Q &= {W_t} - U\\ Q &= T \times l - mgh \end{align*} {/eq}

Here, the work due to tension force is {eq}T {/eq}, initial potential energy is {eq}U {/eq}, the acceleration due to gravity is {eq}g {/eq} and its value is {eq}9.81\;{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\sec }^2}}}} \right. } {{{\sec }^2}}} {/eq}.

Substitute the values in the above equation.

{eq}\begin{align*} Q &= 340\;{\rm{N}} \times 120\;{\rm{m}} - 80\;{\rm{kg}} \times 9.81\;{{\rm{m}} {\left/ {\vphantom {{\rm{m}} {{{\sec }^2} \times }}} \right. } {{{\sec }^2} \times }}30\;{\rm{m}}\\ &= 17256\;{\rm{N}} \cdot {\rm{m}} \end{align*} {/eq}

Thus the thermal energy produced is {eq}17256\;{\rm{N}} \cdot {\rm{m}} {/eq}.