A cart loaded with bricks has a total mass
of 28.5 kg and is pulled at constant speed by
a rope. The rope is inclined at 28.1 ◦ above
the horizontal and the cart moves 13.9 m on
a horizontal floor. The coefficient of kinetic
friction between ground and cart is 0.4 .
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.
To find the work done on the cart by the rope, we can use the formula:
Work = Force * Distance
To calculate the force exerted by the rope, we need to break it down into its components. The force can be broken down into two components: one parallel to the motion of the cart (horizontal) and one perpendicular to the motion of the cart (vertical).
1. Find the force parallel to the motion:
The force parallel to the motion is responsible for overcoming the friction between the ground and the cart.
Friction force = coefficient of kinetic friction * normal force
The normal force is equal to the weight of the cart, which is its mass multiplied by the acceleration due to gravity:
Normal force = mass * gravity
2. Find the vertical force:
The vertical force is responsible for maintaining the equilibrium of the cart on the inclined plane. It can be calculated as follows:
Vertical force = weight of the cart * sin(angle)
3. Calculate the total force:
The total force exerted by the rope is the vector sum of the horizontal and vertical components.
Total force = sqrt((force parallel)^2 + (force vertical)^2)
4. Calculate the work:
The work done on the cart by the rope is given by multiplying the total force by the distance the cart moves.
Work = Total force * Distance
Make sure to convert the final answer to kilojoules (kJ) by dividing by 1000.
Now let's calculate the work done on the cart by the rope step by step:
1. Calculate the friction force:
Friction force = 0.4 * (28.5 kg * 9.8 m/s^2)
2. Calculate the normal force:
Normal force = 28.5 kg * 9.8 m/s^2
3. Calculate the vertical force:
Vertical force = (28.5 kg * 9.8 m/s^2) * sin(28.1°)
4. Calculate the total force:
Total force = sqrt((friction force)^2 + (vertical force)^2)
5. Calculate the work:
Work = Total force * 13.9 m
Finally, divide the work by 1000 to convert it to kilojoules (kJ) to get the final answer.