Two children pull a third child on a tricycle by means of two ropes tied to the

Question

Two children pull a third child on a tricycle by means of two ropes tied to the handlebars. The combined inertia of the child and tricycle is 36 kg . One child pulls with a constant force of 94 N directed to the right of the straight-ahead direction at an angle of 45.

A. If the second child pulls with a force of 80 N, at what angle to the left of the straight ahead direction must he pull to make a tricycle move striaght ahead?

B. With the second child pulling at the angle you calculated in part A, what is the acceleration of the tricycle?

C.what is the work done on the tricycle by the two ropes if the children pull constantly like this while the tricycle moves 2.0m?

Explanation / Answer

here,

mass of cycle and child , mc = 36 kg

force applied to the right , Fr = 94 N

theta = 45 degree

A.

Fl = 80 N

let the angle with the straight be phi

for the tricycle to move in straight direction

Fl * sin(phi) - Fr*sin(theta) = 0

80 * sin(phi) = 94 * sin(45)

phi = 56.19 degree

the direction of Fl must be 56.19 degree left from the straight head

B.

accelration , a = net force / mass

a = ( Fl *cos(phi) + Fr * sin(theta)) / ( mc)

a = ( 80 * cos(56.19) + 94 *cos(45)) / ( 36)

a = 3.08 m/s^2

the accelration of the tricycle is 3.08 m/s^2

C.

the work done on the tricycle , W = Fnet * d

W = ( 80 * cos(56.19) + 94 *cos(45)) * 2

W = 221.97 J

the work done on the tricycle by the two ropes if the children pull constantly like this while the tricycle moves 2.0m is 221.97 J

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