Question

A 4 kg block slides along a frictionless horizontal with a speed of 5.1 m/s. After sliding a distance of 7 m, the block makes a smooth transition to a frictionless ramp inclined at an
angle of 13 degrees to the horizontal.
The acceleration of gravity is 9.81 m/s2.
How far up the ramp does the block slide
before coming momentarily to rest?
Answer in units of m.

Answer 1

Wt. of block=m*g = 4kg * 9.8N/kg=39.2 N.

Et = Ek + Ep = 0.5m*V^2
Ek + Ep = 0.5*4*(5.1)^2 = 52 J.
0 + Ep = 52 @ hmax.
Ep = 52 @ hmax
Ep = mg*h = 52
39.2h = 52
h = 1.33 m.

Dist. up ramp = h/sinA = 1.33/sin13=
5.91 m.