180N
Using Newton's law of motion;
∑F = m x a --------------------(i)
Where;
∑F = Resultant force
m = mass of the object (sled in this case)
a = acceleration of the sled
Calculate the resultant force;
Since the direction of motion is horizontal, the horizontal forces acting on the sled are the;
i. Applied force ([tex]F_{A}[/tex]) in one direction and;
ii. Frictional force ([tex]F_{R}[/tex]) in the other direction to oppose motion
Therefore, the resultant force ∑F is the vector sum of the two forces. i.e;
∑F = [tex]F_{A}[/tex] - [tex]F_{R}[/tex] -----------------------(i)
Frictional force [tex]F_{R}[/tex] is the product of the coefficient of kinetic friction (μ) and weight(W) of the sled. i.e
[tex]F_{R}[/tex] = μ x W
Where;
W = mass(m) x gravity(g)
W = m x g
=> [tex]F_{R}[/tex] = μmg
Substitute [tex]F_{R}[/tex] into equation (ii)
∑F = [tex]F_{A}[/tex] - μmg
Substitute ∑F into equation (i)
[tex]F_{A}[/tex] - μmg = ma -------------------(iii)
Since the motion is at constant speed, it means acceleration is zero (0)
Substitute a = 0 into equation (iii) to give;
[tex]F_{A}[/tex] - μmg = 0
=> [tex]F_{A}[/tex] = μmg
Substitute the values of μ = 0.3, m = 60kg and g = 10m/s² into the above equation to give;
=> [tex]F_{A}[/tex] = 0.3 x 60 x 10
=> [tex]F_{A}[/tex] = 180N
This means that the applied force should be 180N
The amount of force the football player must apply to the sled is 176.4 Newton.
Given the following data:
We know that acceleration due to gravity (g) on Earth is equal to 9.8 [tex]m/s^2[/tex]
To find how much force the football player must apply to the sled:
Mathematically, the force of kinetic friction is given by the formula;
[tex]Fk = umg[/tex]
Where;
Substituting the given parameters into the formula, we have;
[tex]Fk = 0.30\times60\times9.8[/tex]
Force, Fk = 176.4 Newton.
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