# Numerical problems based on the inclined plane physics – solved

In this post, we will focus on numerical problems based on inclined plane physics. We will list down the problems and solve them one by one.

## Numerical problems based on the inclined plane physics

1] A 5-kg mass, initially at rest, slides down a frictionless 30° incline. Calculate the force parallel to the incline and the acceleration of the mass. If the incline is 0.8 m long, calculate the velocity of the mass when it reaches the bottom of the incline.

1] solution:
The goal of the problem is to calculate the desired quantities of force, acceleration, and velocity parallel to the incline (when friction is neglected).

The force parallel to the incline =F= mg sin θ = (5) (9.8) sin 30 = 24.5 N downwards.
Acceleration of the mass =a= g sin θ = (9.8) sin 30 = 4.9 m/s2 downwards
say the velocity of the mass when it reaches the bottom of the incline V and we have to find it out. Then we can use the formula like this:
V2 = U2 + 2 a S
(Here, U =0, acceleration a = 4.9 m/s2 and S = 0.8 m)
So, V = (2 a S)1/2 = (2 x 4.9 x 0.8)1/2 = 2.8 m/s

2 ] A 2-kg mass is sliding down an incline with an unknown angle, as shown. The incline is assumed to be frictionless and is 1.2 m long. The mass starts from rest and is observed to take 2.3 s to reach the bottom. What is the angle of the incline?

Acceleration of the mass along the incline a = g sin θ = 9.8 sin θ …… (1)
We need to use this formula: S = Ut + (1/2) a t2
As, U = 0, the formula becomes: S = (1/2) a t2
=> a = (2 S)/ t2 = (2 x 1.2) /2.32 = 0.45 m/s2 …. (2)
Now from equation 1 and 2:
0.45 = 9.8 sin θ
=> sin θ = 0.45/9.8 = 0.046
=> θ = 2.63 degrees

Numerical problems based on the inclined plane physics – solved
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