A `500kg` horse pulls a cart of mass `1500kg` along a level road with an acceleration of `1m//s^(2)`. if coefficient of sliding friction is `0.2` then force exerted by the earth on horse is .

Options

A. `3000N`
B. `4000N`
C. `5000N`
D. `6000N`

Explanation

To solve the problem, we need to find the force exerted by the Earth on the horse. We will break this down step by step.

### Step 1: Identify the given values
- Mass of the horse (M1) = 500 kg
- Mass of the cart (M2) = 1500 kg
- Total mass (M) = M1 + M2 = 500 kg + 1500 kg = 2000 kg
- Acceleration (a) = 1 m/s²
- Coefficient of friction (μ) = 0.2
- Gravitational acceleration (g) = 9.8 m/s² (approximately)

### Step 2: Calculate the normal force
The normal force (N) acting on the horse and cart system is equal to the total weight of the system, which can be calculated as:
\[ N = M \cdot g = 2000 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 19600 \, \text{N} \]

### Step 3: Calculate the frictional force
The frictional force (F_friction) opposing the motion can be calculated using the formula:
\[ F_{\text{friction}} = \mu \cdot N \]
Substituting the known values:
\[ F_{\text{friction}} = 0.2 \cdot 19600 \, \text{N} = 3920 \, \text{N} \]

### Step 4: Calculate the net force required for acceleration
To find the net force (F_net) required to accelerate the total mass, we use Newton's second law:
\[ F_{\text{net}} = M \cdot a = 2000 \, \text{kg} \cdot 1 \, \text{m/s}^2 = 2000 \, \text{N} \]

### Step 5: Calculate the total force exerted by the horse
The total force (F_total) exerted by the horse must overcome both the frictional force and provide the net force for acceleration:
\[ F_{\text{total}} = F_{\text{friction}} + F_{\text{net}} \]
Substituting the values:
\[ F_{\text{total}} = 3920 \, \text{N} + 2000 \, \text{N} = 5920 \, \text{N} \]

### Step 6: Calculate the force exerted by the Earth on the horse
The force exerted by the Earth on the horse is equal to the weight of the horse plus the force exerted by the horse to pull the cart:
\[ F_{\text{earth on horse}} = M1 \cdot g + F_{\text{total}} \]
Calculating the weight of the horse:
\[ M1 \cdot g = 500 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 4900 \, \text{N} \]
Thus,
\[ F_{\text{earth on horse}} = 4900 \, \text{N} + 5920 \, \text{N} = 10820 \, \text{N} \]

### Final Answer
The force exerted by the Earth on the horse is **10820 N**.

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