.: A 5.0 kg block is moving with constant velocity down a rough incline plane. The coefficients of static and kinetic friction between the block and the incline are 0.25 and 0.20, respectively. What is the inclination angle of the incline plane?
gravity down the plane: mgSinTheta
normal to the plane weight: mgCosTheta
constant velocity, no acceleration...
net force=ma=0
mgSinTheta-mu*mgCosTheta=0
divide both sides by CosTheta
mgTanTheta=mu*mg
theta=arctan mu
of course, mu is the kinetic coefficent.
In a collision, an automobile of mass 826 kg stops with constant acceleration in 20 m from an initial speed of 17 m/s.
What is the acceleration of the car in m/s
12 kg box is sliding down an incline and the coefficient of kinetic friction between the box and the incline is 0.11. Find the angle of the incline where the box slides down with a constant velocity.
To find the inclination angle of the incline plane, we need to analyze the forces acting on the block.
First, let's identify the forces acting on the block. There are two main forces: the gravitational force and the frictional force.
1. Gravitational Force (Weight):
The weight of the block can be calculated using the formula:
Weight (W) = mass (m) x acceleration due to gravity (g)
W = 5.0 kg x 9.8 m/s²
W = 49 N
2. Frictional Force:
There are two types of friction involved: static friction and kinetic friction.
a) Static Friction:
Static friction occurs when the block is not yet moving. The maximum static friction can be calculated using the formula:
Static Friction (Fs max) = coefficient of static friction (μs) x Normal force (N)
Fs max = 0.25 x N
b) Kinetic Friction:
Kinetic friction occurs when the block is moving with constant velocity. The kinetic friction can be calculated using the formula:
Kinetic Friction (Fk) = coefficient of kinetic friction (μk) x Normal force (N)
Fk = 0.20 x N
Now, let's consider the forces in the vertical and horizontal directions:
Vertical Forces:
The vertical forces are the weight of the block (W) and the normal force (N).
Horizontal Forces:
The horizontal forces are the frictional force (F) and the component of the weight parallel to the incline (Wsinθ), where θ is the inclination angle we want to find.
Since the block is moving with constant velocity, there is no net force in the horizontal direction. This means the frictional force (F) is equal to the component of the weight parallel to the incline (Wsinθ).
F = Wsinθ
0.20N = Wsinθ
0.20N = 49Nsinθ
Now, let's find the normal force (N):
Since the block is on an incline, the normal force is not the same as the weight of the block. The normal force can be calculated using the equation:
Normal force (N) = Wcosθ
N = 49Ncosθ
Substitute the value of N in the equation for F:
0.20(49Ncosθ) = 49Nsinθ
Simplify the equation:
0.20cosθ = sinθ
Now, take the inverse sine of both sides of the equation:
arcsin(0.20cosθ) = arcsin(sinθ)
θ = arcsin(0.20cosθ)
Finally, using a scientific calculator or a trigonometric function, you can find the inclination angle (θ) of the incline plane.