Respuesta :
Answer:
The angle between the inclined block and the horizontal surface is 25.16⁰
Explanation:
Given;
mass of block, m = 1.2 kg
force acting parallel to the inclined plane, F = 9 N
frictional force on the block, Fk = 2.8 N.
acceleration of the block. a = 1 m/s²
According to Newtons second law of motion, sum of all the forces acting on the block is given by;
∑F = Ma
F - W - N = ma
where;
F is the parallel force on the block, acting upwards
W is the weight of the block inclined at an angle θ, acting downwards
N is the normal reaction on the block, acting upwards = frictional force on the block.
F - mgsinθ - Fk = ma
9 - (1.2 x 9.8)sinθ - 2.8 = 1.2 x 1
6.2 - 11.76sinθ = 1.2
11.76sinθ = 6.2 - 1.2
11.76sinθ = 5
sinθ = 5 / 11.76
sinθ = 0.4252
θ = sin⁻¹ (0.4252)
θ = 25.16⁰
Therefore, the angle between the inclined block and the horizontal surface is 25.16⁰
Answer:
θ = 25.1°
Explanation:
Given:-
- The force acting on the block, P = 9 N
- The mass of the block, m = 1.2 kg
- The friction force, Ff = 2.8 N
- The acceleration of block, a = 1 m/s^2
Find:-
Determine the angle between the incline and the horizontal surface?
Solution:-
- We will first make a free body diagram of block up an inclined surface at an angle (θ).
- There are three forces acting on the block:
Weight of block (W) : Acts vertically downward
Applied Force (P) : Acts up-hill
Friction force (Ff) : Acts downhill
- We will develop a coordinate system where ( + x ) is up-hill and ( +y) is normal to the inclined surface:
- First we will resolve/transform the Weight (W) which acts downward into a component that acts down the slope.
W = m*g
Wp = m*g*sin(θ)
Where, g: gravitational constant = 9.81 m/s^2
- Apply second Newton equation of motion for the block:
P - Wp - Ff = m*a
9 - 1.2*9.81*sin(θ) - 2.8 = 1.2*1
1.2*9.81*sin(θ) = 5
sin(θ) = 0.42473
θ = 25.1°
Answer: The slope of the inclined surface is θ = 25.1°
