Aclerk moves a box of cans down an aisle by pulling on a strap attached to the box. the clerk pulls with a force of 185.0 n at an angle of 25.0 degrees with the horizontal. the box has a mass of 35.0 kg, and the coefficient of kinetic friction between the box and the floor is 0.450. find the acceleration of the box.

Frictional force opposing the motion of the box due to kinetic friction  is f = un where u is the coefficient of kinetic friction and n the normal force. hence f = (0.450)(35x9.81) = 155 n. the resultant force on the box is fr = 185  cos(25) -  155n = 12.7 n. this is the force accelerating the box. hence the acceleration of the box is fr = ma implies 12.7 n = 35 kg x a, a = 12.7/35 m/s^2 = 0.363 m/s^2

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    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s