Starting from rest, a horse pull a 250-kg cart for a distance of 1,5km. it reaches a speed of 0,38m/s by the time it has walked 50,0m and then walks at constant speed.fictional force 260n.each gram of oats the horse eats releases 9kJ of energy. 10% of this can go into work the horse must do to pull the cart,How many grams of oats must the horse eat to pull the cart?
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To find out how many grams of oats the horse must eat to pull the cart, we need to calculate the total energy required to pull the cart.
First, let's calculate the work done by the fictional force on the horse over the initial 50.0m. Work is given by the equation W = F × d × cos(θ), where F is the force, d is the distance, and θ is the angle between the force and the displacement.
In this case, the force is the fictional force of 260N, the distance is 50.0m, and cos(θ) is equal to 1 (since the force is along the direction of displacement). Therefore, the work done is W = 260N × 50.0m × 1 = 13,000J.
Next, we need to calculate the work done by the horse to pull the cart for the remaining distance of 1.5km (which is equal to 1,500m). The work done is given by the equation W = F × d × cos(θ), where F is the force (which is equal to the frictional force of 260N), d is the distance, and θ is the angle between the force and the displacement.
In this case, the force is still 260N, the distance is 1,500m, and cos(θ) is equal to 1 (since the force is along the direction of displacement). Therefore, the work done is W = 260N × 1,500m × 1 = 390,000J.
Now, let's calculate the total work done by the horse to pull the cart. The horse starts from rest, reaches a speed of 0.38m/s over a distance of 50.0m, and continues to walk at a constant speed. The work done is given by the equation W = (1/2)mv^2, where m is the mass of the cart and v is the final velocity.
In this case, the mass of the cart is 250kg and the final velocity is 0.38m/s. Therefore, the work done is W = (1/2) × 250kg × (0.38m/s)^2 = 14.275J.
The total work done by the horse is the sum of the work done against the fictional force, the work done to pull the cart for the remaining distance, and the work done to reach the final velocity. So, the total work is 13,000J + 390,000J + 14.275J = 403,014.275J.
Now, let's calculate the total energy required, taking into account that only 10% of the energy from the oats can go into work. We need to find the energy that corresponds to 100% of the work done by the horse.
Let E be the energy from the oats required to perform the total work. Since only 10% of the oats' energy can go into work, we have E = 0.10 × 403,014.275J = 40,301.4275J.
Since each gram of oats releases 9kJ of energy, we can convert the energy required into grams by dividing it by 9,000 (9kJ is equal to 9,000J). Therefore, the number of grams of oats required is 40,301.4275J / 9,000J/g = 4.478g (rounded to three decimal places).
Therefore, the horse must eat approximately 4.478 grams of oats to pull the cart.