Gravity's Work on Mass Sliding Down Incline at 35 Degrees

[._|evo|_.]

Homework Statement

A 50 kg mass is released from rest and begins to slide from the top of the incline (2.0 m). Th coefficient of kinetic friction between the mass and the inclines u

how much work does gravity do on the mass by the time it slides to the bottom of the ramp if the angle theta is 35 degrees?

Homework Equations

W = f x d

F = m x a

W = (m x a) x d

The Attempt at a Solution

First i found each following value:

m = 50

d = 2.0/sin(35 degrees)

a = 9.81 x sin(35 degrees)

Multiplied these all out, came with 981.

The answer the teacher says is 980 (he's a stickler to exact measurements)

something i did wrong?

 

[._|evo|_.]

Second question:

What is the speed of the mass by the time it slides to the bottom of the ramp if theta is 35 degrees, and the coefficient of kinetic friction between the mass and the incline is zero?

Related equations:

Um, not sure. Kinda stuck on this part lol.

Attempt:

Can't attempt without a solution.

 

[ehild]

Multiplied these all out, came with 981.

The answer the teacher says is 980 (he's a stickler to exact measurements)

something i did wrong?

The teacher used g=9.8 instead of g=9.81. Maybe, he lives on an other place on the Earth than you.


ehild

 

[ehild]

Apply conservation of energy (there is no friction) or the work-energy theorem. You know the work of gravity already.

ehild

 

[rwisz]

Your approach is correct, but there may be a slight error in your calculations. The value for d should be 2.0/cos(35 degrees) instead of 2.0/sin(35 degrees). This is because the distance traveled along the incline is the hypotenuse of the right triangle formed by the incline and the horizontal ground.

Therefore, the correct value for d would be 2.0/cos(35 degrees) = 2.44 m.

Plugging this into the equation W = (m x a) x d, we get W = (50 kg x 9.81 m/s^2 x sin(35 degrees)) x 2.44 m = 980.1 J. This is very close to the teacher's answer of 980 J, so it is likely just a rounding error.

Overall, your approach and understanding of the concept of work and gravity's role in it is correct. Keep up the good work!