Question

A body of weight 500n is lying on a rough horizontal plane having a coefficient of friction. What is the magnitude of force which can move the body while acting at angle 30 with the horizontal?

Answer 1

To determine the magnitude of the force required to move the body at an angle of 30 degrees with the horizontal, we need to consider the forces acting on the body. In this case, the relevant forces are the gravitational force (weight) acting vertically downward and the frictional force acting horizontally against the motion.

Let's break down the forces and resolve them into their horizontal and vertical components:

1. Weight (mg): The weight of the body is given as 500 N. The weight acts vertically downward, so its vertical component is mg, which is 500 N, and its horizontal component is zero.

2. Frictional force (Ff): The frictional force opposes the motion and acts parallel to the surface. Its magnitude can be calculated using the formula:

   Ff = coefficient of friction × normal force

   Since the body is on a horizontal plane, the normal force (Fn) is equal in magnitude and opposite in direction to the weight (mg), which is 500 N. The coefficient of friction is not provided in the question, so we'll assume a value of μ.

   Ff = μ × Fn = μ × 500 N

Now, we need to find the force required to move the body at an angle of 30 degrees with the horizontal. This force can be determined by resolving it into horizontal and vertical components:

1. Horizontal component: The horizontal component of the force is the force required to overcome friction, so it is equal in magnitude to the frictional force (Ff).

   Fx = Ff = μ × 500 N

2. Vertical component: The vertical component of the force is the force required to balance the weight of the body and keep it on the horizontal plane. Since the body is not accelerating vertically, the vertical component of the force must cancel out the weight.

   Fy = mg = 500 N

Now, we can find the magnitude of the force required to move the body at an angle of 30 degrees with the horizontal by combining the horizontal and vertical components using vector addition:

Magnitude of the force (F) = √(Fx² + Fy²)

F = √((μ × 500 N)² + (500 N)²)

Please note that the exact magnitude of the force required to move the body depends on the coefficient of friction (μ), which is not provided in the question.