A block of mass
lies on a horizontal table. The coefficient of static friction between the block and the table is
.
The coefficient of kinetic friction is
, with
.
Part A
If the block is at rest (and the only forces acting on the block are the force due to gravity and the normal force from
the table), what is the magnitude of the force due to friction?
Hint 1.
Consider the type of friction at rest
What type of friction is acting in this case?

Correct
Part B
Suppose you want to move the block, but you want to push it with the least force possible to get it moving. With
what force
must you be pushing the block just before the block begins to move?
Express the magnitude of
in terms of some or all the variables
,
, and
, as well as the
acceleration due to gravity
.
Hint 1.
Consider the type of friction to start movement
What type of friction is acting in this case?

3/21/2016
Homework 6

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Correct
Part D
Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to
apply the same amount of force even after it starts moving. Find the acceleration
of the block after it begins to
move.
Express your answer in terms of some or all of the variables
,
, and
, as well as the acceleration
due to gravity
.
Hint 1.
Calculate applied force
What is the magnitude
of the force that you are applying to make the block move?

Correct
Part C
Suppose you push horizontally with half the force needed to just make the block move. What is the magnitude of
the friction force?
Express your answer in terms of some or all of the variables
,
, and
, as well as the acceleration
due to gravity
.
Hint 1.
What level of force is required?
In this situation, the force of static friction prevents the object from moving. Therefore, the magnitude of the
static friction force must equal the magnitude of the net horizontal applied force acting on the object, up to a
certain maximum value. In this case,
,
where
is the coefficient of static friction and
is the normal force that the surface exerts on the object.

3/21/2016
Homework 6
Express your answer in terms of some or all of the variables
,
, and
, as well as the
acceleration due to gravity
.

30/31