Question

A cart loaded with bricks has a total mass

of 16.2 kg and is pulled at constant speed by
a rope. The rope is inclined at 31.9° above
the horizontal and the cart moves 30 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°
How much work is done on the cart by the
горе?
Answer in units of kJ.

Answer 1

The work done on the cart by the rope, overcoming friction and pulling the cart 30 m at a constant speed, is approximately 3.402 kJ.

Step-by-step explanation:

To determine the work done on the cart by the rope, we need to consider both the force applied by the rope and the distance over which the force is applied. Since the force is applied at an angle, only the horizontal component of the force actually contributes to the work done on the cart as it moves horizontally on the floor.

The horizontal component of the force (Fhorizontal) can be calculated using the cosine of the angle:

• Fhorizontal = F * cos(θ)

However, the specific force applied by the rope is not given in the problem. Instead, we are provided with the coefficient of kinetic friction (μk) and thus can calculate the force of friction (Ffriction) that the rope must overcome:

• Ffriction = μk * m * g

Where:

• m is the mass of the cart
• g is the acceleration due to gravity

Because the cart is moving at constant speed, the net work done is zero, and the work done by the rope must equal the work done by the frictional force, but in the opposite direction:

• Work = Ffriction * d

Where d is the distance the cart moves. The work done on the cart by the rope will thus be:

• Work = (μk * m * g) * d

Plugging in the values: μk = 0.7, m = 16.2 kg, g = 9.8 m/s2, and d = 30 m, we find:

• Work = (0.7 * 16.2 kg * 9.8 m/s2) * 30 m

Work ≈ 3402.12 J, or 3.402 kJ when converted to kilojoules.

Therefore, the work done on the cart by the rope is approximately 3.402 kJ.