Question

You pull a sled across a horizontal frictionless patch of snow. If your pulling force is in the same direction as the sled's displacement and increases the kinetic energy of the sled by 27%, by what percentage would the sled's kinetic energy increase if the pulling force acted at an angle of 46° above the horizontal?

Answer 1

The kinetic energy of the sled is going to increase by 18.75%

Explanation:

The work W realized by a Force F is given by:

`W=F_x*x`

Where x is the displacement and
`F_x` is the component of the force that is parallel to the displacement.

Additionally, the work is equal to the change in the kinetic energy

`W=K_f-K_i`

If your pulling force is in the same direction as the sled's displacement, we can said that:
`F=F_x`

And if increases the kinetic energy of the sled by 27%, we can said that:

`K_f-K_i=0.27K_i`

So, we can formulate the following equation:

`W=F*x\\W=0.27K_i\\\\F*x=0.27K_i` (1)

On the other hand, if the pulling force acted at an angle of 46° above the horizontal, the work is:

`W=F_x*x=Fcos(46)*x=F*x*cos(46)` (2)

Then, replacing (1) in (2), we get:

`W=F*x*cos(46)=0.27K_i*cos(46) = 0.1875K_i`

Finally, the kinetic energy increase by 18.75% because:

`W=K_f-K_i\\W=0.1875K_i\\\\K_f-K_i=0.1875K_i`