A boy is pushing his sled up a snowy slope. The sled has a mass of 20.4 kg and weighs 200 N. The boy pushes with a constant force of 75 N. The sled travels a distance of 10 m and gains 3 m in height. When the sled reaches the top, it is traveling 2 m/s. What is the efficiency of the slope?

The effeciency of the slope is 0.85 --- 85%

P.E = Wh = 200 N * 3m = 600J P.E
K.E=(1/2)mv^2=(1/2)*20.4 KG*(2m/s)^2=40.8
Total Energy=640.8J
Sled - work done: 75N*10m=750J
Now to find the effeciency
total energy/work done on the sled=640.8J/750J=0.85 *100 =85%

The effeciency of the slope is 0.85 --- 85%

P.E = Wh = 200 N * 3m = 600J P.E
K.E=(1/2)mv^2=(1/2)*20.4 KG*(2m/s)^2=40.8
Total Energy=640.8J
Sled - work done: 75N*10m=750J
Now to find the effeciency
total energy/work done on the sled=640.8J/750J=0.85 *100 =85%

To determine the efficiency of the slope, we need to calculate the work done by the boy in pushing the sled uphill and compare it to the potential energy gained by the sled.

First, let's find the work done by the boy. The work done is given by the formula:

Work = Force * Distance * cos(theta)

Where:
- Force is the magnitude of the force applied by the boy (75 N)
- Distance is the total distance travelled by the sled (10 m)
- theta is the angle between the direction of the force and the direction of motion of the sled. Since it is pushing uphill, the angle is 0 degrees, cos(0) = 1.

Plugging in the values, we get:

Work = 75 N * 10 m * 1 = 750 J

Next, let's calculate the potential energy gained by the sled. The potential energy is given by the formula:

Potential Energy = Mass * Gravity * Height

Where:
- Mass is the mass of the sled (20.4 kg)
- Gravity is the acceleration due to gravity (9.8 m/s^2)
- Height is the change in height of the sled (3 m)

Plugging in the values, we get:

Potential Energy = 20.4 kg * 9.8 m/s^2 * 3 m = 599.04 J

Finally, we can calculate the efficiency using the formula:

Efficiency = (Work output / Work input) * 100%

The work output is the potential energy gained by the sled, and the work input is the work done by the boy.

Efficiency = (599.04 J / 750 J) * 100% ≈ 79.872%

Therefore, the efficiency of the slope is approximately 79.872%.

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