- 1. A 2000 kg loaded coal cart is pulled up at an angle $$ 10^{\circ} $$ inclined at a constant speed by the cable parallel to the incline. The frictional force impeding the motion is 800 N . How much work is done on the cart by the cable as the cart is pulled 30 m . Use $$ g=9.81 \mathrm{~ms} $$.

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To determine the work done on the coal cart by the cable, we'll follow these steps:

1. **Identify the Forces Acting on the Cart:**
   - **Gravitational Force Component Along the Incline:** $$ F_{\text{gravity}} = m \cdot g \cdot \sin(\theta) $$
   - **Frictional Force:** Given as 800 N.
   - **Tension in the Cable ($$ T $$):** Since the cart moves at a constant speed, the tension must balance both the gravitational component and the friction:
     $$
     T = F_{\text{friction}} + F_{\text{gravity}} = 800\, \text{N} + m \cdot g \cdot \sin(10^\circ)
     $$

2. **Calculate the Gravitational Component:**
   $$
   m = 2000\, \text{kg}, \quad g = 9.81\, \text{m/s}^2, \quad \theta = 10^\circ
   $$
   $$
   F_{\text{gravity}} = 2000 \times 9.81 \times \sin(10^\circ) \approx 2000 \times 9.81 \times 0.173648 \approx 3407\, \text{N}
   $$

3. **Determine the Tension in the Cable:**
   $$
   T = 800\, \text{N} + 3407\, \text{N} = 4207\, \text{N}
   $$

4. **Calculate the Work Done by the Cable:**
   Work ($$ W $$) is the product of the force applied in the direction of displacement and the displacement itself:
   $$
   W = T \times d = 4207\, \text{N} \times 30\, \text{m} = 126210\, \text{J}
   $$
   
   Rounding to two significant figures (based on the given data):
   $$
   W \approx 1.26 \times 10^5\, \text{J}
   $$

**Final Answer:**
Approximately 1.26 × 10⁵ joules of work are done by the cable.
The work done by the cable is approximately 126,210 joules.

A 2000 kg loaded coal cart is pulled up at an angle inclined at a
constant speed by the cable parallel to the incline. The frictional force
impeding the motion is 800 N . How much work is done on the cart by
the cable as the cart is pulled 30 m . Use .

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A 2000 kg loaded coal cart is pulled up at an angle inclined at a constant speed by the cable parallel to the incline. The frictional force impeding the motion is 800 N . How much work is done on the cart by the cable as the cart is pulled 30 m . Use .