Mark is pulling his sister in a wagon up a small hill that is at an incline of 15°. If the combined weight of Mark's sister and the wagon is 78 pounds, what is the minimum force required to start moving the wagon up the hill?(Round your answer to the nearest whole number)
Question
Mark is pulling his sister in a wagon up a small hill that is at an incline of 15°. If the combined weight of Mark's sister and the wagon is 78 pounds, what is the minimum force required to start moving the wagon up the hill?(Round your answer to the nearest whole number)
Solution
To solve this problem, we need to use the formula for the force of gravity acting on an object on an incline, which is F = m * g * sin(θ), where:
- F is the force of gravity on the object along the incline,
- m is the mass of the object,
- g is the acceleration due to gravity, and
- θ is the angle of the incline.
First, we need to convert the weight of Mark's sister and the wagon into mass. We can do this by using the formula m = W/g, where W is the weight and g is the acceleration due to gravity. In this case, W = 78 pounds and g = 32.2 ft/s² (the acceleration due to gravity in English units). So, m = 78/32.2 = 2.42 slugs (the unit of mass in the English system).
Next, we need to convert the angle of the incline into radians, since the sin function in the formula uses radians. We can do this by using the formula θ = θ° * π/180, where θ° is the angle in degrees. So, θ = 15° * π/180 = 0.26 radians.
Now we can plug these values into the formula for the force of gravity on an object on an incline:
F = m * g * sin(θ) = 2.42 slugs * 32.2 ft/s² * sin(0.26 radians) = 20.1 pounds.
So, the minimum force required to start moving the wagon up the hill is 20 pounds when rounded to the nearest whole number.
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