A block of mass 2.0 kg is initially at rest on a horizontal surface. The block is pulled a distance of 10 m in 3.0 s by an applied force. The coefficients of static and kinetic friction between the surface and the object are mu _(s)=0.45 and mu _(k)=0.30 respectively. The magnitude of the applied force is most nearly A square B square C square square D

To solve this problem, we need to calculate the magnitude of the applied force required to pull the block a distance of 10 m in 3.0 s, taking into account the forces of friction.<br /><br />Given information:<br />- Mass of the block: 2.0 kg<br />- Distance pulled: 10 m<br />- Time taken: 3.0 s<br />- Coefficient of static friction: μs = 0.45<br />- Coefficient of kinetic friction: μk = 0.30<br /><br />Step 1: Calculate the acceleration of the block.<br />Since the block is initially at rest, the acceleration can be calculated using the kinematic equation:<br />v^2 = u^2 + 2as<br />where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.<br />Since the block is initially at rest, u = 0.<br />v^2 = 2as<br />a = v^2 / (2s)<br />a = (10 m / 3.0 s)^2 / (2 × 10 m)<br />a = 1.85 m/s^2<br /><br />Step 2: Calculate the force of friction.<br />The force of friction is given by:<br />F_friction = μ × N<br />where μ is the coefficient of friction and N is the normal force.<br />Since the block is on a horizontal surface, the normal force is equal to the weight of the block.<br />N = m × g<br />where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2).<br />N = 2.0 kg × 9.8 m/s^2<br />N = 19.6 N<br />F_friction = μ × N<br />F_friction = 0.30 × 19.6 N<br />F_friction = 5.88 N<br /><br />Step 3: Calculate the applied force.<br />The applied force must overcome the force of friction and provide the necessary acceleration to the block.<br />F_applied = F_friction + m × a<br />F_applied = 5.88 N + 2.0 kg × 1.85 m/s^2<br />F_applied = 5.88 N + 3.7 N<br />F_applied = 9.58 N<br /><br />Therefore, the magnitude of the applied force is most nearly 9.0 N (Option B).