Answer:
(a) Coefficient of static friction = 0.709
Coefficient of kinetic friction = 0.471
(b) Force required = 257.5 N
(c) (i) Force required = 51.62 N.
(c) (ii) Acceleration = 3.86 m/s^2
Explanation:
Normal force of the crate = 45 * 9.81 = 441.45 N
Force required to overcome initial friction = 313 N
This would also mean that static frictional force equals 313 N.
Force required to move the crate at constant speed = 208 N
This means that the force of kinetic friction is also 208 N.
(a) Since we know both the normal force, and the static and kinetic frictional forces we can calculate the coefficients of friction as follows:
Static friction = Coefficient of static friction * Normal Force
313 = Coefficient of static friction * 441.45
Coefficient of static friction = 0.709
Kinetic friction = Coefficient of kinetic friction * Normal Force
208 = Coefficient of kinetic friction * 441.45
Coefficient of kinetic friction = 0.471
(b) Since force = mass * acceleration we can calculate the force required as follows:
Force required = 45 * 1.1
Force required = 49.5 N
This would be required ON TOP of the force required to overcome kinetic friction. So the total force required would be:
Force required = 49.5 + 208 = 257.5 N
(c) (i) Since the gravity is less as compared to earth, the normal force will be:
Normal force = mass * gravity
Normal force = 45 * 1.62
Normal force = 72.9
Keeping the same static friction coefficient as (a) we get:
Kinetic friction = 0.709 * 72.9
Kinetic friction = 51.69 N
Thus, the push required for it to move will be 51.62 N.
(c) (ii) Since we know the new normal force, the kinetic friction will be:
Kinetic friction = 0.471 * 72.9
Kinetic friction = 34.34 N
We can now calculate acceleration using the total force as follows:
Total force = mass * acceleration
208 - 34.34 = 45 * acceleration
Acceleration = 3.86 m/s^2
