Concept explainers
(a)
The magnitude of contact force between the two masses.
(a)
Answer to Problem 79P
The magnitude of contact force between the two masses is
Explanation of Solution
Write the expression for the Newton’s second law of motion.
Here,
If the plane is frictionless, then the only force on the two masses are the normal forces and the weight with the frictional forces equalling zero. Since there is no force directed up the incline, the normal force between the two blocks must be zero.
Conclusion:
Therefore, the magnitude of contact force between the two masses is
(b)
The magnitude of contact force between two masses if the coefficient of kinetic friction between the masses and the plane are equal.
(b)
Answer to Problem 79P
The magnitude of contact force between two masses if the coefficient of kinetic friction between the masses and the plane are equal is
Explanation of Solution
Write the expression for the Newton’s law for the mass
Here,
Write the expression for the Newton’s law for the mass
Here,
Use equation (III) to write the expression for
Here,
Use equation (III) in (II) to solve for
Write the expression for the Newton’s law for the mass
Here,
Write the expression for the Newton’s law for the mass
Here,
Use equation (VI) to write the expression for
Here,
Use equation (VII) in (V) to solve for
Write the expression for the Newton’s third law of motion.
If the normal force is non-zero, then the acceleration must be equal.
Use equation (VIII) and (IV) in (X) and it becomes,
The coefficient of kinetic friction between the masses and the plane are equal.
Use equation (XII) in (XI) to solve for the contact forces between the two masses.
The only way this can be true with
Conclusion:
Therefore, the magnitude of contact force between two masses if the coefficient of kinetic friction between the masses and the plane are equal is
(c)
If
(c)
Answer to Problem 79P
The magnitude of contact force between the two blocks is
Explanation of Solution
Use equation (IX) and (XI) to solve for
Conclusion:
Substitute
Therefore, the magnitude of contact force between the two blocks is
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Chapter 4 Solutions
College Physics
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