
Concept explainers
(a)
The normal force applied on the crate by the ramp.
(a)

Answer to Problem 66P
The normal force applied on the crate by the ramp is
Explanation of Solution
The weight of the crate is
The following pic shows the FBD of the system.
The net force along the y-axis is zero as there is no motion in y-axis.
Here,
Re-write the above expression to get an expression for
Conclusion:
Substitute
The normal force applied on the crate by the ramp is
(b)
The magnitude and direction of the interaction partner of the normal force.
(b)

Answer to Problem 66P
The interaction partner of the normal force will have magnitude of
Explanation of Solution
According to the
The normal force on the crate has magnitude of
Conclusion:
The interaction partner of the normal force will have magnitude of
(c)
The static
(c)

Answer to Problem 66P
The static friction force applied between the crate and the ramp is
Explanation of Solution
The weight of the crate is
The following pic shows the FBD of the system.
When the crate is static, the force along the x-axis is zero.
Here,
Re-write the above expression to get an expression for
Conclusion:
Substitute
The static friction force applied between the crate and the ramp is
(d)
The minimum possible value for the coefficient of static friction.
(d)

Answer to Problem 66P
The minimum possible value for the coefficient of static friction is
Explanation of Solution
The weight of the crate is
The following pic shows the FBD of the system.
The minimum coefficient of static friction is just enough to make the friction force equalize the component of weight in the direction of the crate’s motion.
Here,
Write the formula for the coefficient of static friction.
Here,
Write the formula for the normal force.
Substitute equation (III) and (V) in equation (IV).
Conclusion:
Substitute
The minimum possible value for the coefficient of static friction is
(e)
The magnitude and direction of the contact force exerted on the crate by the ramp.
(e)

Answer to Problem 66P
The magnitude of the contact force is
Explanation of Solution
The weight of the crate is
The friction force and the normal force are the component of the contact force.
Write the formula for the magnitude of the contact force.
Here,
Write the direction of the contact force.
Here
Conclusion:
Substitute
Substitute
The magnitude of the contact force is
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