Final velocity of the mass on an incline?

[titolydia]

A spring with a spring-constant 3.4 N/cm
is compressed 27 cm and released. The 9 kg
mass skids down the frictional incline of height
13 cm and inclined at a 17◦ angle.
The acceleration of gravity is 9.8 m/s2 .
The path is frictionless except for a dis-
tance of 0.5 m along the incline which has a
coefficient of friction of 0.2.


What is the final velocity vf of the mass?

 

[Hootenanny]

A spring with a spring-constant 3.4 N/cm
is compressed 27 cm and released. The 9 kg
mass skids down the frictional incline of height
13 cm and inclined at a 17◦ angle.
The acceleration of gravity is 9.8 m/s2 .
The path is frictionless except for a dis-
tance of 0.5 m along the incline which has a
coefficient of friction of 0.2.


What is the final velocity vf of the mass?

What have you tried thus far? What are the relevant equations?

We have a homework template for a reason, please use it!

 

[nlightner]

Based on the given parameters, the final velocity of the mass can be calculated using the principles of energy conservation. The initial potential energy of the compressed spring will be converted into kinetic energy as the mass slides down the incline. The equation for this can be written as:

PE = KE

Where PE is the potential energy and KE is the kinetic energy. The potential energy can be calculated as:

PE = mgh

Where m is the mass (9 kg), g is the acceleration of gravity (9.8 m/s^2), and h is the height of the incline (13 cm). Therefore, PE = (9 kg)(9.8 m/s^2)(0.13 m) = 11.31 J.

The kinetic energy can be calculated as:

KE = 1/2 mv^2

Where m is the mass (9 kg) and v is the final velocity. Therefore, KE = (1/2)(9 kg)v^2.

Since energy is conserved, we can equate PE and KE and solve for v:

PE = KE

11.31 J = (1/2)(9 kg)v^2

v^2 = 2(11.31 J)/(9 kg)

v = √(2(11.31 J)/(9 kg))

v = 1.89 m/s

Therefore, the final velocity of the mass on the incline is 1.89 m/s. This calculation assumes that there is no friction along the incline. However, since there is a distance of 0.5 m with a coefficient of friction of 0.2, the final velocity may be slightly lower due to the work done by friction.