Answer in units of J.
Henry
answered
Fk = u*Fc = 0.442 * 218.54 = 96.6 N. =
Force of kinetic friction.
Fap*cos27.3-Fk = m*a
Fap*cos27.3-96.6 = m*0 = 0
Fap*cos27.3 = 96.6 N.
W=Fap*cos27.3 * d = 96.6 * 9.3=898.3 J.
Fap = Force applied = Tension in rope.
Henry
answered
Fk = u*Fc-u*Fap*sin27.3
Fk = 0.442*218.54 - 0.442*Fap*sin27.3
Fk = 96.6 - 0.203Fap
Fap*cos27.3-(96.6-0.203Fap) = m*a
0.889Fap - 96.6 + 0.203Fap = m*0 1.092Fap = 96.6
Fap = 88.5 N. = Force applied.
W = Fap*cos27.3 * d
W = 88.5*cos27.3 * 9.3 = 731.3 J.
Explain Bot
answered
First, let's find the force exerted by the rope. The force exerted by the rope can be divided into two components: a horizontal component and a vertical component.
The vertical component of the force is equal to the weight of the cart, which can be calculated as follows:
Weight = mass * gravity
Weight = 22.3 kg * 9.8 m/s^2
Weight = 218.54 N (Newtons)
The horizontal component of the force is equal to the force required to overcome the kinetic friction between the cart and the ground. This can be calculated as follows:
Frictional force = coefficient of kinetic friction * normal force
Normal force = mass * gravity * cos(theta)
Frictional force = 0.442 * (22.3 kg * 9.8 m/s^2 * cos(27.3 degrees))
Frictional force = 82.51 N
Now, let's find the force exerted by the rope:
Force by rope = sqrt(horizontal force^2 + vertical force^2)
Force by rope = sqrt((Frictional force)^2 + (Weight)^2)
Force by rope = sqrt((82.51 N)^2 + (218.54 N)^2)
Force by rope = 237.17 N
Finally, let's calculate the work done by the rope:
Work = force * distance
Work = 237.17 N * 9.3 m
Work = 2205.68 J
Therefore, the work done on the cart by the rope is 2205.68 Joules (J).
