A cart loaded with bricks has a total mass

of 25.4 kg and is pulled at constant speed by
a rope. The rope is inclined at 30.6

above
the horizontal and the cart moves 18.4 m on
a horizontal floor. The coefficient of kinetic
friction between ground and cart is 0.7 .
The acceleration of gravity is 9.8 m/s
2
.
How much work is done on the cart by the
rope?
Answer in units of kJ

Wc = m * g = 25.4kg * 9.8N/kg = 249 N.=

Weight of cart.

Fap*cosA-Fk = m * a
Fap*cos30.6 -0.7*249 = m*0 = 0
Fap*cos30.6 = 174.3
Fap = 174.3/cos30.6 = 202.5 N. = Force
applied.

Work = Fap * d = 202.5 * 18.4 = 3726 J.=
3.726 kJ.

To find the work done on the cart by the rope, we need to calculate the force exerted by the rope and multiply it by the distance the cart is pulled.

First, let's find the force exerted by the rope. The only force acting on the cart in the horizontal direction is the force of friction, since the cart is pulled at constant speed. The force of friction can be calculated using the equation:

Frictional force = coefficient of friction * normal force

The normal force is the force exerted by the ground on the cart, which is equal to the weight of the cart (mass * acceleration due to gravity). So, the normal force can be calculated as:

Normal force = mass * acceleration due to gravity

Next, we need to calculate the force exerted by the rope. This force has a vertical component (opposing gravity) and a horizontal component. The vertical component can be found using the equation:

Vertical force = force of gravity * sin(angle of incline)

And the horizontal component can be found using the equation:

Horizontal force = force of gravity * cos(angle of incline)

Since the cart is pulled at constant speed, the horizontal force exerted by the rope is equal in magnitude and opposite in direction to the force of friction. So, the horizontal force exerted by the rope is equal to the force of friction.

Now, we can calculate the force of friction and the horizontal force exerted by the rope:

Force of friction = coefficient of friction * normal force
Horizontal force = Force of friction

Finally, we can calculate the work done by the rope:

Work = force * distance

Substituting the values and applying the appropriate unit conversions, we can find the work done on the cart by the rope in units of kJ.