Dr. Naumoff - AP Physics 1– chapter 6
Setup practice problems 1-5(Not all variables listed may required for the answer.
All scenarios take place on the planet Earth).
1. A block is sliding down an incline that forms an angle θ with the horizontal.
The mass of the block is m. The coefficient of friction between the block and
the inclined plane is µk.
a. Draw a sketch of the system.
b. Draw a free body diagram for the system.
c. Derive the expression for the downslope acceleration using m,g
,µk,and θ.
d. Derive the expression for µk using the appropriate quantities and a for
acceleration.
e. Derive the expression for the downslope acceleration in the absence of
friction.
2. A block with a mass of m1 is attached to a string that goes over a massless
pulley and is attached to a hanging mass m2. The block with a mass of m1 is
sliding along a horizontal surface. The coefficient of friction between the
block and the surface is µk.
a. Draw a sketch of the system.
b. Draw a free body diagram for each of the masses.
c. Derive the expression for the acceleration of the system.
d. Derive the expression for the tension in the rope.
e. Derive the expression for µk using the appropriate quantities and a for
acceleration.
f. Derive the expression for the acceleration in the absence of friction.
g. Derive the expression for the tension in the rope in the absence of
friction.
3. A block with a mass of m1 is attached to a string that is attached to a block
with a mass of m2. A second string attached to the other side of m2 goes over
a massless pulley and is attached to a hanging mass m3. The blocks with the
masses of m1 and m2 are sliding along a horizontal frictionless surface. The
string between m1 and m2 is undergoing a tension of T1. The string between
m2 and m3 is undergoing a tension of T2.
a. Draw a sketch of the system.
b. Draw a free body diagram for each of the masses.
c. Derive the expression for the acceleration of the system.
d. Derive the expression for T1.
e. Derive the expression for T2.
4. A block with mass m is sliding along a horizontal surface. The block is
attached to a string that is at an angle θ above the horizontal. The tension in
the string is T. The coefficient of friction between the block and the surface
is µk.
a. Draw a sketch of the system.
b. Draw a free body diagram for the mass.
c. Derive the expression for the acceleration of the system.
d. Derive the expression for T in terms of µk, a, m, g, and θ.
5. A block with mass m is sliding along a horizontal surface. The block is
undergoing a force F is at an angle θ below the horizontal. The coefficient of
friction between the block and the surface is µk.
a. Draw a sketch of the system.
b. Draw a free body diagram for the mass.
c. Derive the expression for the acceleration of the system.
Dr. Naumoff - AP Physics 1– chapter 6 Setup practice problems (6-10)
6. A car is moving along a horizontal track in a circular path with a radius r.
The car’s velocity is v and µs is the coefficient of static friction between the
track and the tires.
a. Draw a free body diagram for the car.
b. Derive the expression for the maximum velocity that the car can attain
before it begins to skid.
c. What is supplying the centripetal force?
7. A car is going over a bump in the road. The bump is an arc of a circle with
the radius r. The mass of the car is m and its velocity is v.
a. Derive the equation for the apparent weight of the car.
b. What is the necessary condition for the apparent weight of the car to
be equal to zero.
c. What are several other scenarios where the above logic would apply?
8. A car is going through a dip in the road. The dip is an arc of a circle with the
radius r. The mass of the car is m and its velocity is v.
a. Derive the equation for the apparent weight of the car.
b. What is the necessary condition for the apparent weight of the car to
be equal to zero.
c. What are several other scenarios where the above logic would apply?
9. A bucket of mass m is attached to a rope and is being whirled in a vertical
circle with a constant velocity.
a. Derive an equation for the tension T in the rope at the top of the circle.
b. Derive an equation for the tension T in the rope at the bottom of the
circle.
10. An object is sliding along a horizontal surface with an initial velocity v o.
The coefficient of friction between the block and the surface is µk.
a. Draw a free body diagram for the object.
b. Derive the expression for the acceleration of the object.
c. Derive the expression for the distance traveled by the object before it
stops.