a body rolled on a surface with speed of 10m/s comes to rest after covering distance of 50 m find cofficient of friction
v^2 - u^2 = 2as
0-100=2*a*50
-100/100=a
a=-1 m/s^2
Negative sign shows reduction.
let n be the coeff. of friction,
n*mg=m*a
n=a/g
n=1/9.8
n=0.102
Good
Well, that's quite a persistent body! It really knows how to stop and smell the roses... or in this case, stop and calculate the coefficient of friction.
To find the coefficient of friction, we need to know the initial velocity, the distance covered, and the final velocity (in this case, zero). We can use the equation:
final velocity^2 = initial velocity^2 + 2 * acceleration * distance
Since the final velocity is zero, we can simplify the equation to:
0 = initial velocity^2 + 2 * acceleration * distance
Given that the initial velocity is 10 m/s and the distance is 50 m, we can rearrange the equation to solve for acceleration:
acceleration = -initial velocity^2 / (2 * distance)
Plugging in the values, we get:
acceleration = -(10 m/s)^2 / (2 * 50 m)
Simplifying further:
acceleration = -100 m^2/s^2 / 100 m
acceleration = -1 m/s^2
Now, the coefficient of friction can be calculated using the formula:
frictional force = coefficient of friction * normal force
In this case, since the body is coming to rest, the frictional force is equal in magnitude to the force applied by the body's weight (mg). Since we don't have information about the object's mass, we can't calculate the normal force directly. However, we can ignore it for now and assume it cancels out during calculation.
frictional force = mass * acceleration
Since we don't know the mass, we can assume it as 1 kg.
frictional force = 1 kg * -1 m/s^2
frictional force = -1 N
And since the frictional force is equal to the coefficient of friction multiplied by the normal force (which cancels out), we can conclude:
coefficient of friction = frictional force / normal force = -1 N / (1 kg * 9.8 m/s^2) ≈ -0.1
So, the coefficient of friction is approximately -0.1. But I have to say, that's a negative surprise! Maybe it's time for that body to get a grip and find a more positive coefficient of friction.
To find the coefficient of friction, we can use the equation that relates the force of friction to the normal force and the coefficient of friction. The equation is:
Force of Friction = (Coefficient of Friction) x (Normal Force)
In this case, the normal force is equal to the weight of the body, since it is on a horizontal surface. The weight can be calculated using the formula:
Weight = Mass x Gravitational Acceleration
First, let's find the weight of the body. Since the body comes to rest, the force of friction must have caused it to decelerate. The net force acting on the body is given by:
Net Force = Mass x Acceleration
Since the body comes to rest, the acceleration is equal to zero. Therefore, the net force is also zero. The force of friction acts in the opposite direction to the motion, so we have:
Force of Friction = Mass x Acceleration = 0
Now let's find the normal force:
Weight = Mass x Gravitational Acceleration
Since the body is at rest on a horizontal surface, the gravitational force is equal to the normal force:
Weight = Normal Force
Now we can rewrite the equation for the force of friction as:
Force of Friction = (Coefficient of Friction) x (Weight)
Since the body is at rest, the force of friction is equal to the force that caused it to stop. This force is the initial kinetic energy of the body which is related to its mass and velocity:
Force of Friction = 0.5 x Mass x (Velocity)^2
Now we can equate the two expressions for the force of friction:
0.5 x Mass x (Velocity)^2 = (Coefficient of Friction) x (Mass x Gravitational Acceleration)
We can cancel out the mass on both sides:
0.5 x (Velocity)^2 = (Coefficient of Friction) x (Gravitational Acceleration)
Now we can rearrange the equation to solve for the coefficient of friction:
Coefficient of Friction = (0.5 x (Velocity)^2) / (Gravitational Acceleration)
Substituting the given values:
Velocity = 10 m/s
Gravitational Acceleration = 9.8 m/s^2
Coefficient of Friction = (0.5 x (10)^2) / (9.8)
Coefficient of Friction = 0.51 (approximately)
Therefore, the coefficient of friction is approximately 0.51.