Friction Concepts Homework: True or False Answers

[gummybeargirl]

Homework Statement

A mass M is initially at rest on a horizontal surface, μs=0.30 and μk=0.20 . A horizontal string then pulls M with a tension T. N is the normal component of the contact force. All quantities below are magnitudes.
True or False:
1) If M does not accelerate, then T ≤ μsN
2) M will accelerate if T exceeds μkN
3) M will accelerate if T exceed μsN
4) The value of N equals Mg
5) T equals μkN if M remains at rest.
6) The total force on M is μkN if M remains at rest.

2. The attempt at a solution
From what i have learned i thought the answer should be:
1) True (to gain acceleration, first F must exceed μsN)
2) True (it takes µkN, force to just move M, and anything over that will accelerate M)
3) True
4) True (mg = N, the normal force)
5) False (T is less than or equal to µsN for M not to move)
6) False (The total force on M is equal to or less than µsN for no movement)
The in incorrect but i am not sure as to why they are wrong.

 

[dauto]

looks good

 

[gummybeargirl]

The correct answers are actually
1) True
2) False (It must exceed ukN not just uks)
3) True
4) True
5) False
6) False

 

[Nathanael]

The correct answers are actually
2) False (It must exceed ukN not just uks)

The actual reason (which you may have meant to say) is it must exceed u$_{s}$N, not u$_{k}$N

 

[HalfLostAndSearching]

Your answers are mostly correct, but there are a few errors. Here are the correct answers:
1) True
2) False (M will not accelerate unless T is greater than or equal to μkN)
3) True
4) True
5) True
6) True

For question 2, the statement says "M will accelerate if T exceeds μkN", which is not necessarily true. M will only accelerate if T is greater than or equal to μkN.

For question 5, the statement says "T equals μkN if M remains at rest", which is true because T can be equal to μkN and M will still remain at rest.

For question 6, the statement says "The total force on M is μkN if M remains at rest", which is also true because the total force on M can be equal to μkN and M will still remain at rest.