Batpenguin sees the penguinsignal and leaps into the penguinmobile, which is at rest in the icy penguincave on a smooth
Posted: Mon May 23, 2022 11:43 am
Batpenguin sees the penguinsignal and leaps into the
penguinmobile, which is at rest in the icy penguincave on a smooth
and unsloped slippery floor with static friction
coefficient μS= 0.2.
1. The penguinmobile has a mass of m = 1.3x10^2kg and the
penguincave is just beneath the surface of the Earth with
gravitational acceleration downward at g 9.8 m/s^2.
Batpenguin wants to accelerate as fast as possible to get to the
scene of the crime, but doesn't want to slip on the icy floor. What
is the maximum force (in Newtons) that the bottoms of the wheels
can exert on the ground to push the car forward without slipping
when Batpenguin stomps on the accelerator?
2. What is the maximum acceleration of the penguinmobile
(in m/s^2) that Batpenguin can achieve without the wheels
slipping?
3. The road out of the penguincave is L = 100 m
long and flat until the very end, where there is the start to a
ramp up to a jump across the penguinmoat. From experience,
Batpenguin knows that she needs the penguinmobile to be traveling
at least 18 m/s at the bottom of the ramp in order to make the
jump. If the penguinmobile keeps constant maximum acceleration
(before slipping as in the previous problem) for the entire 100 m
road, will Batpenguin make the jump? (True = Yes, False = No.
Assume the penguinmobile is so slick and advanced that it does not
experience drag from air resistance. Explain your answer in the
write-up.) (T/F)
4. After traveling the full 100 m length at constant
acceleration, Batpenguin reaches the bottom of the ramp, which
tilts up from the horizontal. While going up the ramp Batpenguin
notices that despite having the same constant acceleration forward
(parallel to the ramp), the speed of the car is also remaining
constant while on the ramp. By what angle (in radians) must the
ramp be tilted upwards for this to be true?
5. Batpenguin reaches the top of the ramp (still moving at
the same speed as when the penguinmobile reached the bottom of the
ramp) and becomes airborne. Since the wheels don't help much while
in the air, there's not much for Batpenguin to do so she enjoys the
aerial scenery. What is the maximum height above the end of the
ramp (in meters) that the penguinmobile reaches before it starts to
come down again? (ignore air resistance)
6. Still bored with the penguinmobile in the air,
Batpenguin notices that it takes twice as much time to reach the
final height of the landing platform from the maximum height as it
took to reach the maximum height from the end of the ramp. At what
height below the end of the ramp is the landing platform (in
meters, as a positive magnitude of the height displacement)?
7. While waiting for the penguinmobile to land, Batpenguin
breaks the fourth wall and does some dimensional analysis about her
own situation. She notices that the only given variables for this
problem have been μS, m, L, and g, so all answers
must be expressible as functions of only these four variables. The
final height of the platform below the end of the ramp from the
previous problem is a length in meters. Batpenguin concludes that
the expression for the change in height must have the
form |h_f - h_i| = CμSkL for some
constant C and some unknown power k of the
dimensionless friction coefficient. (In your write-up, explain how
Batpenguin reached this conclusion.) Without more detailed
calculations, Batpenguin is unable to find the constant and power
before the car lands.
Help out Batpenguin by revisiting your own derivations. If you
don't plug in numbers and solve for the final height difference
between the landing platform and the end of the ramp in terms of
only μS and L, what values of the
constant C and the power k do you find in the
final expression? (Hint: This question should be quick to
answer if you did not plug in numbers too early in the preceding
problems.)
A. C = 2, k = 1
B. C = 1, k = 1
C. C = 3, k = 3
D. C = 3, k = 2
E. C = 2, k = 2
penguinmobile, which is at rest in the icy penguincave on a smooth
and unsloped slippery floor with static friction
coefficient μS= 0.2.
1. The penguinmobile has a mass of m = 1.3x10^2kg and the
penguincave is just beneath the surface of the Earth with
gravitational acceleration downward at g 9.8 m/s^2.
Batpenguin wants to accelerate as fast as possible to get to the
scene of the crime, but doesn't want to slip on the icy floor. What
is the maximum force (in Newtons) that the bottoms of the wheels
can exert on the ground to push the car forward without slipping
when Batpenguin stomps on the accelerator?
2. What is the maximum acceleration of the penguinmobile
(in m/s^2) that Batpenguin can achieve without the wheels
slipping?
3. The road out of the penguincave is L = 100 m
long and flat until the very end, where there is the start to a
ramp up to a jump across the penguinmoat. From experience,
Batpenguin knows that she needs the penguinmobile to be traveling
at least 18 m/s at the bottom of the ramp in order to make the
jump. If the penguinmobile keeps constant maximum acceleration
(before slipping as in the previous problem) for the entire 100 m
road, will Batpenguin make the jump? (True = Yes, False = No.
Assume the penguinmobile is so slick and advanced that it does not
experience drag from air resistance. Explain your answer in the
write-up.) (T/F)
4. After traveling the full 100 m length at constant
acceleration, Batpenguin reaches the bottom of the ramp, which
tilts up from the horizontal. While going up the ramp Batpenguin
notices that despite having the same constant acceleration forward
(parallel to the ramp), the speed of the car is also remaining
constant while on the ramp. By what angle (in radians) must the
ramp be tilted upwards for this to be true?
5. Batpenguin reaches the top of the ramp (still moving at
the same speed as when the penguinmobile reached the bottom of the
ramp) and becomes airborne. Since the wheels don't help much while
in the air, there's not much for Batpenguin to do so she enjoys the
aerial scenery. What is the maximum height above the end of the
ramp (in meters) that the penguinmobile reaches before it starts to
come down again? (ignore air resistance)
6. Still bored with the penguinmobile in the air,
Batpenguin notices that it takes twice as much time to reach the
final height of the landing platform from the maximum height as it
took to reach the maximum height from the end of the ramp. At what
height below the end of the ramp is the landing platform (in
meters, as a positive magnitude of the height displacement)?
7. While waiting for the penguinmobile to land, Batpenguin
breaks the fourth wall and does some dimensional analysis about her
own situation. She notices that the only given variables for this
problem have been μS, m, L, and g, so all answers
must be expressible as functions of only these four variables. The
final height of the platform below the end of the ramp from the
previous problem is a length in meters. Batpenguin concludes that
the expression for the change in height must have the
form |h_f - h_i| = CμSkL for some
constant C and some unknown power k of the
dimensionless friction coefficient. (In your write-up, explain how
Batpenguin reached this conclusion.) Without more detailed
calculations, Batpenguin is unable to find the constant and power
before the car lands.
Help out Batpenguin by revisiting your own derivations. If you
don't plug in numbers and solve for the final height difference
between the landing platform and the end of the ramp in terms of
only μS and L, what values of the
constant C and the power k do you find in the
final expression? (Hint: This question should be quick to
answer if you did not plug in numbers too early in the preceding
problems.)
A. C = 2, k = 1
B. C = 1, k = 1
C. C = 3, k = 3
D. C = 3, k = 2
E. C = 2, k = 2