Question

A block of mass 2.0 kg and an initial speed of 5.4ms−1 slides on a rough horizontal surface and is eventually brought to rest after travelling a distance of 4.0 m. Calculate the frictional force between the block and the surface.

Answer 1

You are given the initial velocity ($v_{i}$), the final velocity ($v_{f}$) and the distance (d).

First thing to do is get the acceleration. Therefore, we will use the kinematic formula:

$v_{f}^2=v_{i}^2+2ad\\(5.4)^2=0^2+2a*4\\a=\frac{(5.4)^2}{8}=3.645\:m/s^2$

Friction is a force, therefore it is calculated as: F = ma

F = 2*3.645 = 7.29 N

Answer 2

Given:

Mass = 2 kg

Initial velocity = 5.4 m / s

Distance = 4 m

To find:

The frictional force between the block and the surface

Solution:

To find the acceleration,

By formula,

Final velocity^2 = Initial velocity^2 * 2 * Acceleration * Distance

Substituting,

Acceleration = ( 5.4 )^2 / 8

Acceleration = 3.64 m / s

Hence,

Friction = Mass * Acceleration

2 * 3.64

Friction = 7.2 N

Hence, the frictional force between the block and the surface is 7.2 N