A block of mass 10-kg is pulled on a horizontal floor by applying a force of F at an angle of 30o with the horizontal. The block moves along the floor with an acceleration of 0.1 m/s2. The coefficient of kinetic friction is 0.2. What is the magnitude of F?
Question
A block of mass 10-kg is pulled on a horizontal floor by applying a force of F at an angle of 30o with the horizontal. The block moves along the floor with an acceleration of 0.1 m/s2. The coefficient of kinetic friction is 0.2. What is the magnitude of F?
Solution
To solve this problem, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The net force is the vector sum of all the forces acting on the object.
Step 1: Identify the forces acting on the block The forces acting on the block are:
- The weight of the block (W = m*g, where m is the mass and g is the acceleration due to gravity)
- The normal force (N) exerted by the floor on the block
- The frictional force (f = μ*N, where μ is the coefficient of kinetic friction)
- The applied force (F)
Step 2: Resolve the applied force into its horizontal and vertical components The horizontal component of F is Fcos(30) and the vertical component is Fsin(30).
Step 3: Apply Newton's second law in the vertical direction The net force in the vertical direction is zero because the block is not moving vertically. So, N - W - F*sin(30) = 0. We can solve this equation for N.
Step 4: Apply Newton's second law in the horizontal direction The net force in the horizontal direction is the total force in the direction of motion minus the frictional force. So, Fcos(30) - f = ma. We can substitute f = μ*N into this equation and solve for F.
Let's plug in the given values: m = 10 kg, a = 0.1 m/s², μ = 0.2, and g = 9.8 m/s².
Step 3: N = mg + Fsin(30) Step 4: Fcos(30) - μN = m*a
These are two equations with two unknowns (F and N). You can solve these equations simultaneously to find the value of F.
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