A cart loaded with bricks has a total mass

of 18 kg and is pulled at constant speed by
a rope. The rope is inclined at 30.4 � above
the horizontal and the cart moves 21.5 m on
a horizontal floor. The coefficient of kinetic
friction between ground and cart is 0.8 .
The acceleration of gravity is 9.8 m/s2 .
How much work is done on the cart by the
rope?
Answer in units of kJ

2 answers

Calculate the rope tension from the information given.
Call it T.

The horizontal component of T = Friction force
since it does not accelerate.

(M*g - T sin21.5) *0.8 = T cos 21.5

Solve for T

Work done by rope = T*cos30.4*21.5 m
T*cos(θ) = Ffr –––> Ffr = µk* Fn –––>
Fn = m*g - T*sin(θ) :

T*cos(θ) = ( µk*(m*g - T*sin(θ) )

T*cos(30.4º) = (0.8 *(18*9.8 – T*sin(30.4º))

T*cos(30.4º) = 88.2 N – 0.8 * T *sin(30.4º)

T*cos(30.4º) + 0.8*T*sin(30.4º) = 141.12 N

T (cos(30.4º) + 0.8*sin(30.4º)) = 141.12 N

T = 141.12 N / (cos(30.4º) + 0.8*sin(30.4º))

T = 111.4 N

-------------------------

Work = T*cos(θ)*d

W = 111.4*cos(30.4º)*21.5m = 2065.81 J or 2.07 kJ
Similar Questions
  1. Three part problem cant figure out the second and third parts(part 1 of 3) A cart loaded with bricks has a total mass of 12.9 kg
    1. answers icon 2 answers
  2. A cart loaded with bricks has a total massof 28.5 kg and is pulled at constant speed by a rope. The rope is inclined at 28.1 ◦
    1. answers icon 0 answers
    1. answers icon 6 answers
  3. A cart loaded with bricks has a total massof 25.4 kg and is pulled at constant speed by a rope. The rope is inclined at 30.6 ◦
    1. answers icon 1 answer
more similar questions