A block of mass 4.6 kg slides 15 m from rest down an inclined plane making an angle of 20 o with the horizontal. If the block takes 10 s to slide down the plane, what is the retarding force due to friction?
To find the retarding force due to friction, we need to calculate the acceleration of the block first.
1. Identify the given values:
- Mass of the block (m) = 4.6 kg
- Distance traveled (s) = 15 m
- Angle with the horizontal (θ) = 20°
- Time taken (t) = 10 s
2. Calculate the acceleration:
The block is sliding down an inclined plane, so the force of gravity can be separated into two components:
- The component of the force acting parallel to the plane (mg sinθ) causes acceleration.
- The component of the force acting perpendicular to the plane (mg cosθ) cancels out with the normal force.
The equation for acceleration in this case is given by:
a = (2s - ut^2) / (t^2)
Plug in the values: s = 15 m, u = 0 m/s (since the block starts from rest), and t = 10 s.
a = (2 * 15 - 0 * (10^2)) / (10^2)
a = (30) / 100
a = 0.3 m/s²
3. Calculate the retarding force due to friction:
The retarding force due to friction can be calculated using the equation:
Frictional force (F) = mass (m) * acceleration (a)
Plug in the values: m = 4.6 kg and a = 0.3 m/s²
F = 4.6 kg * 0.3 m/s²
F = 1.38 N
Therefore, the retarding force due to friction is 1.38 N.