crate of mass m1�1 slides down a well-lubricated hill of height hℎ, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass.
A crate of mass m1�1 slides down a well-lubricated hill of height hℎ, with negligible friction. At the bottom, where it is moving horizontally, it collides with another crate, of mass m2, that initially was sitting at rest and that is attached to a wall by a spring of spring constant k that initially is at its equilibrium length. Assume that the spring itself has negligible mass.
a) Write an equation that expresses the speed v of the crate when it arrives at the bottom of the hill in terms of the height of the hill and other known quantities.
b) When the two crates collide, they stick together, due to Velcro pads pasted on their mating surfaces. Write an equation that expresses the speed v2 of the two crates after the collision, in terms of the speed v of crate m1 just before the collision.
c)As the coupled crates continue to move to the right, they compress the spring by a distance d, at which point they momentarily stop. Assuming that the coefficient of kinetic friction between the crates and the floor is μ, write an expression for the work done by friction while the crates are sliding in terms of the distance d and other known quantities.
d)Given that the distance d that the crates compress the spring is d=0.35 m, calculate the speed v2 of the crates immediately after the collision, in units of meters per second. Use the following values: k=950N/m, m1=2.4kg, m2=2.6kg, μ=n0.49, g= 9.8 m/s^2
e) What was the speed of the crate of mass m1�1 just before the collision with the second block, in meters per second?
f) What is the height h of the hill, in meters?
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