A girl lifts her 20-kg knapsack a vertical distance of 0.70 m and then she carries it 2510 m across the park to the water fountain. The value of the work done by the girl is __________ J.
20 * 9.81 * .7
no work is done carrying. Force is not in direction of motion
A girl lifts her 18-kg knapsack a vertical distance of 0.55 m and then she carries it 2510 m across the park to the water fountain. The value of the work done by the girl is
To find the work done by the girl, we need to calculate the work done in lifting the knapsack and the work done in carrying it across the park.
The work done in lifting the knapsack can be calculated using the formula:
Work (W) = Force (F) × Distance (d) × Cos(θ)
In this case, the force exerted by the girl is equal to the weight of the knapsack, which can be calculated using the formula:
Force (F) = Mass (m) × Gravity (g)
Given that the mass (m) of the knapsack is 20 kg and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can calculate the force:
Force (F) = 20 kg × 9.8 m/s^2 = 196 N (rounding to two significant figures)
The distance (d) lifted vertically is 0.70 m.
Finally, the angle (θ) between the direction of the force and the direction of displacement is 0 degrees since the force and displacement are in the same direction.
Now, we can calculate the work done in lifting the knapsack:
Work (W) = 196 N × 0.70 m × Cos(0°)
Cos(0°) = 1
Work (W) = 196 N × 0.70 m × 1 = 137.2 J
The work done in lifting the knapsack is 137.2 Joules (J).
Next, we need to calculate the work done in carrying the knapsack across the park. The formula for work is the same:
Work (W) = Force (F) × Distance (d) × Cos(θ)
In this case, the force exerted by the girl is equal to zero since there is no vertical displacement. Therefore, the work done in carrying the knapsack across the park is zero.
Adding the work done in lifting the knapsack (137.2 J) and the work done in carrying it across the park (0 J):
Total Work (W) = 137.2 J + 0 J = 137.2 J
Therefore, the value of the work done by the girl is 137.2 Joules (J).
To calculate the work done by the girl in this scenario, we need to use the formula:
Work (W) = Force (F) * Distance (d) * Cosine of the angle (θ) between the force and the displacement.
In this case, we are given the weight of the knapsack (20 kg) as the force applied by the girl. We know that the force due to gravity is equal to the weight, which can be calculated as:
Force (F) = mass (m) * acceleration due to gravity (g)
F = 20 kg * 9.8 m/s^2 ≈ 196 N
Now, let's calculate the work done while lifting the knapsack:
Work (lifting) = Force (F) * Distance (d) * Cosine of the angle (θ)
Given:
Force (F) = 196 N
Distance (d) = 0.70 m
Since the girl lifts the knapsack vertically, the angle between the force and displacement is 0 degrees. The cosine of 0 degrees is 1.
Therefore:
Work (lifting) = 196 N * 0.70 m * 1
Work (lifting) ≈ 137.2 J
Now, let's calculate the work done while carrying the knapsack:
Work (carrying) = Force (F) * Distance (d)
Given:
Force (F) = 196 N
Distance (d) = 2510 m
Work (carrying) = 196 N * 2510 m
Work (carrying) ≈ 491,560 J
To find the total work done, we need to add the work done while lifting and the work done while carrying:
Total Work = Work (lifting) + Work (carrying)
Total Work ≈ 137.2 J + 491,560 J
Total Work ≈ 491,697.2 J
Therefore, the value of the work done by the girl is approximately 491,697.2 Joules (J).