Question
An object is subject to a force that varies with position suchthat from x=0 to x=5.00 m the force increases linearly from 0 to3.00N, from x=5.00m to x=10.00 m the force is constant at 3.00N andfrom x= 10.00m to 17.00 m the force decreases linearly from 3.00Nto 0. A. Find the work done by the force on the object as the objectmoves from x=0 to x=5.00 m B. x=5.00m to x=10.00 m C. x=10.00 m to x=17.00 m D. Find the total work done. E. If the object in this problem has a mass of 3.00 kg and avelocity of /500 m/s at x=0, find its velocity when it has traveled10.0 m with the above forces applied to it. An object is subject to a force that varies with position suchthat from x=0 to x=5.00 m the force increases linearly from 0 to3.00N, from x=5.00m to x=10.00 m the force is constant at 3.00N andfrom x= 10.00m to 17.00 m the force decreases linearly from 3.00Nto 0. A. Find the work done by the force on the object as the objectmoves from x=0 to x=5.00 m B. x=5.00m to x=10.00 m C. x=10.00 m to x=17.00 m D. Find the total work done. E. If the object in this problem has a mass of 3.00 kg and avelocity of /500 m/s at x=0, find its velocity when it has traveled10.0 m with the above forces applied to it.
Explanation / Answer
A.the work done by the force on the object as the object movesfrom x = 0 to x = 5.00 m is W = F * S F = 3.00 N and S = (5.00 - 0) m = 5.00 m or W = 3.00 * 5.00 = 15 J B.the work done by the force on the object as the object movesfrom x = 5.00 m to x = 10.00 m is W1 = F1 * S1 F1 = 3.00 N and S1 = (10.00 - 5.00) m =5.00 m or W1 = 3.00 * 5.00 = 15 J C.the work done by the force on the object as the object movesfrom x = 10.00 m to x = 17.00 m is W2 = F2 * S2 F2 = 0 N and S2 = (17.00 - 10.00) m= 7.00 m or W2 = 0 * 7.00 = 0 J D.The total work done is E = W + W1 + W2 or E = 15 + 15 + 0 = 30 J E.According to the law of conservation of energy wehave or E = 15 + 15 + 0 = 30 J E.According to the law of conservation of energy wehave K1 + U1 = K2 + U2 or (1/2)m * v12 + m * g * x1= (1/2)m * v22 + m * g * x2 or (1/2)m * v22 = [(1/2)m *v12 + m * g * x1 - m * g *x2] or (1/2)m * v22 = m *[(1/2)v12 + g * x1 - g *x2] or v2 = [2((1/2)v12 + g *x1 - g * x2)]1/2 or v2 = [2((1/2)v12 + g *(x1 - x2))]1/2 v1 = 500 m/s,g = 9.8 m/s2,x1= 0 and x2 = 10.0 m v1 = 500 m/s,g = 9.8 m/s2,x1= 0 and x2 = 10.0 m