A little red wagon with mass 7.00 kg moves in a straight line on a frictionless horizontal surface. It has an initial speed of 4.00 m/s and then is pushed 3.0 m in the direction of the initial velocity by a force with a magnitude of 10.0 N. (a) Use the work–energy theorem to calculate the wagon’s final speed. (b) Calculate the acceleration produced by the force. Use this acceleration in the kinematic relationships of Chapter 2 to calculate the wagon’s final speed. Compare this result to that calculated in part (a).
Solution 27E Step 1: Data given Mass m = 7.00 kg Initial velocity vi= 4.00 m/s Distance travelled x = 3.00 m Force exerted F = 10.0 N We need to find the final speed of wagon wheel Let us find the work done The work done by the applied force over the 3.00 m distance It is obtained using W = Fx Substituting the values we get W = 10.0 N × 3.00 m W = 30.0 J Thus we have work done = 30.0 J As per the work energy relations We can write 2 2 W = 1/2 mv 1i2 mv f Substituting we get 2 2 30 J = 1/2 × 7.0 kg × (4 m/s) 1/2 × 7.0 kg × v f Rearranging and solving we get 2 v = 2(30J)+7.00 kg ×(4 m/s) 7.00 kg 2((30J)+7.00 kg ×(4 m/s) ) v = 7.00 kg v = 4.96 m/s Step 2: We need to find the acceleration produced by the force We know F = m × a Since we need to find acceleration We shall rearrange to get a = F/m Substituting values we get a = 10.0 N /7 kg 2 a = 1.43 m/s Thus we have acceleration as 1.43 m/s 2