A body weight 500 newton is lying on a rough horizontal plane if the coefficient between the body and the horizontal surface is 0.525 find the magnitude of the force is acting at an angle of 28 with the horizontal
To find the magnitude of the force acting on the body at an angle of 28 degrees with the horizontal, we need to resolve the weight force into two components: one along the horizontal direction and the other along the vertical direction.
First, let's find the weight force acting vertically. The weight force can be calculated by multiplying the body's mass by the acceleration due to gravity (g = 9.8 m/s^2). So, the weight force (Fw) can be calculated as:
Fw = mass * g
Given that the mass is not provided in the question, we can use the relationship between weight and mass: weight = mass * gravity. Therefore, the weight force (Fw) can be calculated as:
Fw = 500 N
Next, let's find the horizontal component of the weight force. The horizontal component can be calculated by multiplying the weight force by the coefficient of friction (μ) between the body and the horizontal surface. So, the horizontal component force (Fh) can be calculated as:
Fh = Fw * μ
Given that the coefficient of friction (μ) is 0.525, the horizontal component force (Fh) can be calculated as:
Fh = 500 N * 0.525
Fh = 262.5 N
Finally, we can find the magnitude of the force at an angle of 28 degrees with the horizontal. This force is the resultant force of the weight force (Fw) and the horizontal component force (Fh). We can use the concept of vector addition to find the resultant force (Fr). The magnitude of the resultant force can be calculated using the Pythagorean theorem:
Fr = √(Fw^2 + Fh^2)
Substituting the values we calculated:
Fr = √(500^2 + 262.5^2)
Fr ≈ 570.43 N
Therefore, the magnitude of the force acting at an angle of 28 degrees with the horizontal is approximately 570.43 N.