A man is pulling a block with a mass of 6.2 kg across a horizontal surface and accelerates the block at a
rate of 0.50 m/s2
. The coefficient of kinetic friction between the block and the surface is 0.24. What is
the magnitude of the force with which the man pulls?
To find the magnitude of the force with which the man pulls, we need to consider the forces acting on the block.
The force of kinetic friction (fk) can be calculated using the formula:
fk = μk * N
Where μk is the coefficient of kinetic friction and N is the normal force.
The normal force (N) can be calculated as the weight of the block (mg) since the block is on a horizontal surface and there is no vertical acceleration:
N = mg
The force with which the man pulls (F) can be calculated using Newton's second law of motion:
F = m * a
Substituting the given values:
m = 6.2 kg (mass of the block)
a = 0.50 m/s^2 (acceleration of the block)
μk = 0.24 (coefficient of kinetic friction)
g = 9.8 m/s^2 (acceleration due to gravity)
First, calculate the weight of the block:
mg = 6.2 kg * 9.8 m/s^2 = 60.76 N
Next, calculate the normal force:
N = mg = 60.76 N
Then, calculate the force of kinetic friction:
fk = μk * N = 0.24 * 60.76 N = 14.58 N
Finally, calculate the magnitude of the force with which the man pulls:
F = m * a = 6.2 kg * 0.50 m/s^2 = 3.1 N
Therefore, the magnitude of the force with which the man pulls is 3.1 N.