Thermal Energy created by block sliding down ramp

[ccflyfisher]

1. A 1300 N crate slides 15 m down a ramp that makes an angle of 40 degrees with the horizontal.


2. F _therm = F_k[tex]\Delta[/tex][tex]X[/tex]


3. I understand how to solve this with the coefficient of friction given, but how can I without the problem stating [tex]\mu[/tex]?

 

[vela]

Without more information, you can't.

 

[Vixiel]

You can solve this because to get a constant velocity down the ramp, there must be 0 net acceleration. You can solve for the acceleration down the ramp due to gravity but doing gsin([tex]\theta[/tex]),or 9.8m/s²*sin(40[tex]\circ[/tex]), which gives you 6.3m/s². Since this is the acceleration downwards, friction must produce the same acceleration up the ramp to produce the constant velocity. Simply multiply this acceleration by the mass of the object (1300N/9.8m/s²=132.653), then by 15 meters.
You get about 12534.358 J, or 1.3*10⁴.

 

[vela]

Who said anything about the crate moving at constant velocity?

 

[rwisz]

I would like to clarify that thermal energy is not directly created by the block sliding down the ramp. The force of gravity acting on the block causes it to accelerate down the ramp, and this kinetic energy is converted into thermal energy due to friction between the block and the ramp.

To solve this problem without the coefficient of friction, we can make some assumptions. First, we can assume that the surface of the ramp is rough enough to create a significant amount of friction. This means that the coefficient of friction is likely to be relatively high, and we can use a value of 0.5 as a reasonable estimate.

Next, we can use the formula for calculating kinetic energy, which is KE = 1/2 * m * v^2. We know the mass of the crate (1300 N) and the distance it travels (15 m), so we can calculate its final velocity using the formula for acceleration (a = g * sinθ) and the equation v^2 = u^2 + 2as, where u is the initial velocity (0 m/s) and s is the displacement (15 m).

Once we have the final velocity, we can use it to calculate the kinetic energy of the crate. We can then use the formula for work (W = F * d) to determine the amount of work done by the frictional force, which is equal to the change in kinetic energy.

Finally, we can use the formula for thermal energy (Q = m * c * ΔT) to calculate the amount of thermal energy produced, where m is the mass of the crate, c is the specific heat capacity of the material, and ΔT is the change in temperature. We can assume that the temperature change is negligible, so the thermal energy will be equal to the work done by friction.

In summary, while it is not possible to calculate the exact amount of thermal energy without knowing the coefficient of friction, we can make reasonable assumptions and use relevant formulas to estimate it.