a body is pulled over a surface by applying 20 Newton making an angle 60 degree with the horizontal.if the body moves with constant speed on a rough surface on which coefficient of friction is .4 then the mass of the body is?
horizontal pull = 20 cos 60 = 10 N
vertical pull up = 20 sin 60 = 17.3 N
normal force = m g - 17.3
friction force = .4 (9.81 m - 17.3)
= 3.92 m - 6.92
so
3.92 m - 6.92 = 10
To find the mass of the body, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force pulling the body over the surface is 20 Newtons, and it makes an angle of 60 degrees with the horizontal. We can resolve this force into two components: the vertical component and the horizontal component.
The horizontal component of the force, Fx, will be given by F*cos(theta), where F is the magnitude of the force (20 N) and theta is the angle (60 degrees). Therefore, Fx = 20 N * cos(60) = 20 N * 0.5 = 10 N.
The vertical component of the force, Fy, will be given by F*sin(theta), where F is the magnitude of the force (20 N) and theta is the angle (60 degrees). Therefore, Fy = 20 N * sin(60) = 20 N * 0.866 = 17.32 N.
Since the body is moving at a constant speed, we can assume that the net force acting on it is zero. In other words, the frictional force acting on the body must be equal in magnitude and opposite in direction to the horizontal force.
The frictional force, Ff, can be calculated using the formula Ff = μ * N, where μ is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the body, which is given by N = mg, where m is the mass of the body and g is the acceleration due to gravity (9.8 m/s^2).
Since the body is at rest on the horizontal surface, the vertical component of the force (Fy) must balance the weight of the body. Therefore, Fy = N = mg.
Substituting the value of N into the equation for the frictional force, we get Ff = μ * mg.
Since the net force is zero, Fx = Ff. Therefore, we have Fx = μ * mg.
Substituting the values we know, we get:
10 N = 0.4 * m * 9.8 m/s^2.
Simplifying the equation, we find:
10 N = 3.92 m.
Dividing both sides by 3.92, we get:
m ≈ 2.55 kg.
Therefore, the mass of the body is approximately 2.55 kg.