A block a mass of .113 kg is slid horizontally with a acceleration of 2.612 m/s^2 What is the kinectic force and the coefficient of friction. Please show the steps in getting these answers,
F=ma
F=F(fr)=>
ma=μmg
μ=a/g
Thank you
For your help You don't know how much its doin
To find the kinetic force and the coefficient of friction, we need to apply Newton's second law of motion and consider the forces acting on the block.
1. Determine the net force acting on the block:
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Therefore, the net force (F_net) can be calculated as follows:
F_net = mass × acceleration
Given:
mass (m) = 0.113 kg
acceleration (a) = 2.612 m/s^2
F_net = 0.113 kg × 2.612 m/s^2
F_net = 0.296456 kg⋅m/s^2 (rounded to 3 decimal places)
2. Calculate the kinetic force:
The kinetic force (F_kinetic) is the force required to overcome the friction acting on the block. In this case, there are no other horizontal forces acting on the block except for the force of friction. Therefore, the kinetic force is equal to the net force.
F_kinetic = F_net
F_kinetic = 0.296456 kg⋅m/s^2 (rounded to 3 decimal places)
3. Determine the coefficient of friction:
The force of friction (F_friction) can be calculated using the equation:
F_friction = coefficient of friction × normal force
In this scenario, the block is sliding horizontally, so the normal force (F_normal) acting on the block is equal to its weight (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_normal = mass × acceleration due to gravity
F_normal = 0.113 kg × 9.8 m/s^2
F_normal = 1.1084 kg⋅m/s^2 (rounded to 4 decimal places)
Now, rearranging the equation for friction:
F_friction = coefficient of friction × F_normal
Since F_kinetic is equal to F_friction:
F_kinetic = coefficient of friction × F_normal
Rearranging for coefficient of friction:
coefficient of friction = F_kinetic / F_normal
coefficient of friction = 0.296456 kg⋅m/s^2 / 1.1084 kg⋅m/s^2
coefficient of friction ≈ 0.2673 (rounded to 4 decimal places)
Therefore, the kinetic force is approximately 0.296456 kg⋅m/s^2, and the coefficient of friction is approximately 0.2673.