1.A 40.0 kg wagon is towed up a hill inclined at 19 degree with respect to the h

Question

1.A 40.0 kg wagon is towed up a hill inclined at 19 degree with respect to the horizontal. the tow rope is parallel to the incline and has a tension of 140N. Assume that the wagon starts from rest at the bottom of the hill, and neglect friction. How fast is the wagon going after 81m up the hill? answer in m/s

2. Two objests with masses of 3.0kg and 5.0kg are connected by a light sring that passes over a frictionless pulley.
a) determine the tension in the string. N
b)determine the acceleration of each object. m/s2
c) Determine the distance each object will move in the first second of motion both objects start from rest.

Explanation / Answer

Given mass of the wagon, m = 40 kg Angle of inclination,? = 19^0 Length of the hill, s = 81 m Tension in the rope,T = 140N Net force on the rope is F = T - mgsin19    = 140N - 40 kg *9.8 m/s^2 * 0.325 F = 12.3 N According to work energy theorem W = KEf -KEi F *S = 1/2 mv^2 12.3N *81 m = 0.5 *40 kg *v^2 v = 7.05 m/s is the speed of the wagon -------------------------------------------------------------------- m1 = 3 kg, m2 = 5 kg The net force on m1 is m1a = T -m1g----(1) Net force on m2 is m2a = m2g - T T = m2g - m2a substitute value of T in 1 m1a = m2g - m2a - m1g a(m1 +m2) = g( m2 -m1) a = g( m2 -m1)/(m1 +m2)    = 9.8 m/s^2 (5kg -3 kg)/(5 kg +3 kg) a = 2.45 m/s^2 ------------------------------------------------------------ a)Tension in each string is ,T = m2 (g -a) T = 5 kg( 9.8 m/s^2 - 2.45 m/s^2)      = 36.75 N b) Acceleration in each object , a = 2.45 m/s^2 c)The distance each object moved is       s = 1/2at^2          = 0.5 *2.45 m/s^2 *(1 s)^2       s = 1.2 m

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