HOW FAR UP THE INCLINE DOES THE Monkey MOVE?

Question

Initial speed of 2.0 m/s
up a 24.0° incline
mass is 14 kg
Coefficient of kinetic friction is 0.20.

How far up the incline does it move? In m?

Answer 1

The answer would be 0.346m along the ramp. If you are looking for how high he goes, it's 0.140m.

The forces that would be acting on him are gravity, normal force, and friction. We want to find the ones that decelerate him in the direction of the ramp. If you rotated your axis and made the ramp the x-axis, then this makes it easier. The force of gravity's component in the direction of the ramp is then Fgsin(24). Friction is along the ramp, and we need to know the normal force to find it. To find the normal force, setting the x-axis along the ramp also helps. Since the monkey is not acceleratting perpindicular to the ramp, Fnormal=Fgcos(24). Ffriction=Fnormal x u. Ffriction = Fgcos(24) x u. So the forces acting on him in the direction of the ramp are now
Fgsin(24)
Fgcos(24)u -------> Fnet = Fgsin(24) + Fgcos(24)u
Fg = mg and Fnet = ma ---------> ma = mgsin(24) + mgcos(24)u

The m's then cancel out.

a = 9.8sin(24) + 9.8cos(24) x 0.2 = 5.777 m/s/s

This acceleration would be negative b/c it is in the opposite direction of his velocity. The farthest up the monkey will reach the ramp is when his velocity reaches zero. So, we can use the equation

Vf² = Vi² + 2ax
0 = 2² + 2 (-5.777)x
x = 0.346m

This distance is along the ramp, if you want height, just use trig identities.

Answer 2

commonly used reaction (perpendicular to floor) is mg Cos ? = sixteen x 9.80 one x Cos 22 = one hundred forty five.5 N Friction tension = µR = 0.2 x one hundred forty five.5 = 29.11N To push weight against gravity, tension = mgSin ? = sixteen x 981 x Sin 22 = fifty 8.8 N for this reason finished opposing tension = 29.11 + fifty 8.8 = 87.9N Opposing tension = mass x deceleration (Newton's 2d regulation) - 87.9 = sixteen a a = - 5.40 9 m/s^2 Vf = 0 Vi = 3 s = ? Vf^2 = Vi^2 - 2 x 5.40 9 x s 0 = 9 - 10.99s 10.99s = 9 s = 9 / 10.ninety 9 = 0.819 metres up the incline

Answer 3

Does the monkey continue trying to climb the ramp? That would change things.