Question

What force is needed to accelerate a sled ( mass = 55 kg) at$\mathbf{1}\mathbf{.}\mathbf{4}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$on horizontal frictionless ice?

Short answer

The force needed to accelerate the sled is 77 N.

Step-by-step solution

Step 1. Significance of Newton’s second law on a sled

This law states that the force acting on the sled depends on its mass and acceleration.

The product of the mass and acceleration of the sled gives the force required to accelerate the given sled.

If the mass value of the sled can be increased, then the sled's acceleration would decrease.

Step 2. Identification of given data 

The given data can be listed below as:

• The mass of the sled is $m=55\mathrm{kg}$.
• The acceleration of the sled is $a=1.4\mathrm{m}/{\mathrm{s}}^2$.
• The surface is frictionless, so the friction value is considered as zero.

Step 3. Determination of the force needed to accelerate the sled

From Newton’s second law, the force required to accelerate the sled can be calculated as:

$F=ma$

Here, m is the mass of the sled, and a is the acceleration of the sled.

Substitute the values as 55 kg for m, and $1.4\mathrm{m}/{\mathrm{s}}^2$for a in the above equation.

$\begin{array}{c}F=55\mathrm{kg}\times 1.4\mathrm{m}/{\mathrm{s}}^2\left(\frac{1\mathrm{N}}{1\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2}\right)\\ =77\mathrm{N}\end{array}$

Thus, the force needed to accelerate the sled is 77 N.