Find the coeffecient of kinetic friction between a 3.85kg block and the horizontal surface on which it rests if at 85 N/m spring must be stretched by 6.20cm to pull it with constant speed. Assume that the spring pulls in the horizontal direction.
To find the coefficient of kinetic friction between the block and the horizontal surface, we can use Hooke's law and the equation for the force of kinetic friction.
First, let's identify the relevant information given in the problem:
- Mass of the block (m): 3.85 kg
- Spring constant (k): 85 N/m
- Displacement of the spring (x): 6.20 cm = 0.0620 m
According to Hooke's law, the force exerted by the spring is given by:
F_spring = k * x
Substituting the given values:
F_spring = 85 N/m * 0.0620 m
F_spring = 5.27 N
Now, the force of kinetic friction (F_friction) can be calculated using the equation:
F_friction = μ * N
where μ is the coefficient of kinetic friction and N is the normal force.
Since the block is resting on a horizontal surface, the normal force is equal in magnitude but opposite in direction to the force of gravity acting on the block. Thus,
N = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given mass:
N = 3.85 kg * 9.8 m/s^2
N = 37.73 N
Now, we can calculate the coefficient of kinetic friction by rearranging the equation for frictional force:
F_friction = μ * N
Solving for μ:
μ = F_friction / N
Substituting the values we found earlier:
μ = 5.27 N / 37.73 N
μ ≈ 0.1397
Therefore, the coefficient of kinetic friction between the block and the horizontal surface is approximately 0.1397.