# Math Help - Conservation of Energy

1. ## Conservation of Energy

There is a 3Kg crate at the bottom of an incline, initially moving at $3 m.s^{-1}$. The incline is 20 degrees and frictionless. The crate moves through a displacement of d metres and comes to a stop. Calculate d.

I did the following:

$(E_{p} + E_{k})_{Bottom} = (E_{p} + E_{k})_{Top}$
$0 + {1/2}.(3).(3)^2 = (3).(9.8).Sin20.d + 0$
$d = 1.34m$

Is this correct?

2. Originally Posted by MarcoMP
There is a 3Kg crate at the bottom of an incline, initially moving at $3 m.s^{-1}$. The incline is 20 degrees and frictionless. The crate moves through a displacement of d metres and comes to a stop. Calculate d.

I did the following:

$(E_{p} + E_{k})_{Bottom} = (E_{p} + E_{k})_{Top}$
$0 + {1/2}.(3).(3)^2 = (3).(9.8).Sin20.d + 0$
$d = 1.34m$

Is this correct?
HI

From the principle of conservation of energy , PE gained = KE lost

$\frac{1}{2}mu^2=\frac{1}{2}mv^2+mgh$

$\frac{1}{2}(3)(3)^2=0+(3)(9.81)(d\sin 20)$

$d=1.341$