Question

Mech. 2. 2m Bumper The cart shown above is made of a block of mass 2m. The cart is released from rest and rolls without slipping from the top of an inclined plane of height $h$. Express all algebraic answers in terms of the given quantities and fundamental constants. a) Determine the total energy in the cart-Earth-spring system. b) Derive an expression for the speed of the cart when it reaches the bottom of the incline. c) After rolling down the incline and across the horizontal surface the cart collides with a bumper of negligible mass attached to an ideal spring, which has a spring constant $k$. Derive an expression for the distance the spring is compressed before the cart and bumper come to rest. d) Now assume the bumper has non-negligible mass. After the collision with the bumper, the spring is compressed to a maximum distance of about 90% of the value found in part c) Give a reasonable explanation for this decrease.

          Mech. 2.
2m
Bumper
The cart shown above is made of a block of mass 2m. The cart is released from rest and rolls
without slipping from the top of an inclined plane of height $h$. Express all algebraic answers in
terms of the given quantities and fundamental constants.
a) Determine the total energy in the cart-Earth-spring system.
b) Derive an expression for the speed of the cart when it reaches the bottom of the incline.
c) After rolling down the incline and across the horizontal surface the cart collides with a
bumper of negligible mass attached to an ideal spring, which has a spring constant $k$.
Derive an expression for the distance the spring is compressed before the cart and
bumper come to rest.
d) Now assume the bumper has non-negligible mass. After the collision with the bumper,
the spring is compressed to a maximum distance of about 90% of the value found in part
c) Give a reasonable explanation for this decrease.

Mech. 2.
2m
Bumper
The cart shown above is made of a block of mass 2m. The cart is released from rest and rolls
without slipping from the top of an inclined plane of height h. Express all algebraic answers in
terms of the given quantities and fundamental constants.
a) Determine the total energy in the cart-Earth-spring system.
b) Derive an expression for the speed of the cart when it reaches the bottom of the incline.
c) After rolling down the incline and across the horizontal surface the cart collides with a
bumper of negligible mass attached to an ideal spring, which has a spring constant k.
Derive an expression for the distance the spring is compressed before the cart and
bumper come to rest.
d) Now assume the bumper has non-negligible mass. After the collision with the bumper,
the spring is compressed to a maximum distance of about 90% of the value found in part
c) Give a reasonable explanation for this decrease.

Added by Jason C.

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