A @0N crate starting at rest slides down a rough 5.0m ramp, inclined at 25 degress with the horizontal. 20j of energy is lost due to friction. what will be the speed of the crate at the bottom of the incline?
i need some help these one i don't know where to start
Is your @0N (the weight, M g) supposed to be 20N? I will assume so. If not, you provide the correct value.
The loss in potential energy is
M g * 5 sin 25 meters = 42.3 J
PE loss = friction + kinetic energy gain
42.3 = 20 + KE increase = (1/2) M V^2
(1/2) M V^2 = 22.3 J
M = 20 N/9.8 = 2.04 kg
V^2 = 2*22.3/2.04 m^2/s62
solve for V
To find the speed of the crate at the bottom of the incline, you can use the principle of conservation of mechanical energy. The total mechanical energy of the system (crate + Earth) remains constant unless acted upon by external forces. In this case, the only external force is friction, which causes a loss of energy.
The mechanical energy of the crate can be given by the sum of its kinetic energy (KE) and potential energy (PE):
Initial Mechanical Energy = KE + PE
The initial kinetic energy of the crate is zero since it starts at rest: KE(initial) = 0.
The initial potential energy of the crate is given by: PE(initial) = m * g * h
where m is the mass of the crate, g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical height of the incline.
The final mechanical energy at the bottom of the incline is given by:
Final Mechanical Energy = KE(final) + PE(final)
Since all the initial mechanical energy is lost due to friction (20 J), the final mechanical energy is reduced:
Final Mechanical Energy = Initial Mechanical Energy - Energy Loss
Final Mechanical Energy = 0 - 20 J
At the bottom of the incline, the potential energy is zero (PE(final) = 0) since the crate is at ground level. Therefore, we can rewrite the equation as:
0 - Energy Loss = KE(final)
Now, we can set up the equation for the final kinetic energy of the crate:
KE(final) = (1/2) * m * v^2
where v is the final velocity of the crate.
We can rewrite the equation as:
-20 J = (1/2) * m * v^2
Now, you can solve for the velocity (v) of the crate at the bottom of the incline by plugging in the given values for energy loss (20 J), mass (m), and rearranging the equation.