Question

There is a variable amount of friction between a block of mass m and a ramp at an angle θ above the horizontal. The kinetic and static coefficients of friction are equal but vary as µ=Ax, where x is measured along the ramp and x = 0 is the bottom of the ramp. The block is sent up the ramp with an initial speed v0, and comes to a stop somewhere on the ramp. In the following parts, take your “system” to be the block, the rough ramp, plus its interaction with the Earth through the gravitational field.

. If v0 is small, then the block will slide back down after it comes to rest. Find the smallest value of v0 such that after coming to rest at the top, the block does not slide back down.

Answer #1

A block of mass m1 begins at the bottom of a ramp that is
inclined an angle θ above the horizontal. It is initially moving up
the ramp with velocity v0. A second block of mass m2 is at rest on
the ramp a distance d up the ramp from the ﬁrst block. Friction
keeps the second block from sliding down. The coeﬃcient of kinetic
friction between the ramp and the blocks is µk for both
blocks.
What is the...

A 5.00-kg 5.00-kg block is sent up a ramp inclined at an angle
?= 25.0 ∘ θ=25.0∘ from the horizontal. It is given an initial
velocity ? 0 =15.0 m/s v0=15.0 m/s up the ramp. Between the block
and the ramp, the coefficient of kinetic friction is ? k =0.50
μk=0.50 and the coefficient of static friction is ? s =0.60.
μs=0.60. What distance ? D along the ramp's surface does the block
travel before it comes to a stop?

A block of mass 19.6 kg starts at rest at the top of a
frictionless ramp that makes an angle of 36.2 ^\circ ∘ below the
horizontal. After it slides without friction down the entire 2.89 m
length of the ramp, it begins to slide horizontally along a rough
concrete surface with a coefficient of kinetic friction of
\mu_kμ k = 0.503 until it slows to a complete
stop. How far does the block slide horizontally along the concrete
before...

A block (4 kg) starts from rest and slides down
a frictionless ramp #1 of height 9 m. The block
then slides a horizontal distance of 1 m on a
rough surface with kinetic coefficient of friction
μk = 0.5. Next, it slides back up
another frictionless ramp #2.
Find the following numerical energy values:
Initial gravitational potential energy on Ramp #1: U1G
= J
Tries 0/3
Kinetic energy at bottom of Ramp #1 before
traveling across the rough surface: K...

A 5.00-kg5.00-kg block is sent up a ramp inclined at an angle
?=28.0∘θ=28.0∘ from the horizontal. It is given an initial velocity
?0=15.0 m/sv0=15.0 m/s up the ramp. Between the block and the ramp,
the coefficient of kinetic friction is ?k=0.50μk=0.50 and the
coefficient of static friction is ?s=0.60.μs=0.60.
What distance ?D along the ramp's surface does the block travel
before it comes to a stop?

A 1.2-kg block, travelling at 14.2-m/s, encounters a
ramp with a coefficient of kinetic friction of 0.15. The ramp is
tilted 31° above the horizontal. Use work and energy arguments to
answer the following.
How far along the ramp does the block travel?
Assume the coefficient of static friction is very
small and the block slides back down the ramp. What is its speed at
the bottom?

A 30 kg block is put on a ramp of angle θ = 30o with
coefficients of static friction 0.3 and kinetic friction 0.2; a
force F1 = 150N is applied to the block to try to stop
it from sliding down, but the force is applied directed at an angle
of θ1 = 60o counterclockwise from the ramp
upward incline
a) On the drawing draw the forces and their components
b) Derive the formula for the Normal force and...

A block with mass m1 = 8.8 kg is on an incline with
an angle θ = 40° with respect to the horizontal. For the first
question there is no friction, but for the rest of this problem the
coefficients of friction are: μk = 0.38 and
μs = 0.418.
1. When there is no friction, what is the magnitude of the
acceleration of the block?
2. Now with friction, what is the magnitude of the acceleration
of the block...

A block of mass 16.31 kg is initially held at rest on a 25.94
degree incline. The coefficient of static friction is 0.3472 and
the coefficient of kinetic friction is 0.2083.
A) Find: mg, FDH, FN, fsmax, and fk and express them rounded to
the nearest full Newton.
B) What is the minimum force up the ramp that will keep the
block from sliding down?
C) What is the maximum force up the ramp you can exert before
the block...

Ramp Angle is 37 degrees Mass is 5.0 kg Initial Velocity is 3.0
m/s Coefficient of Kinetic Friction is 0.6 Coefficient of Static
Friction is 0.8
Questions:
• What is value of each force that acts on the block?
•What is net force and acceleration of object?
• What distance does it travel along the ramp before
stopping?
• When block stops, will it stay at rest or start moving back
down?
Please show all work

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