Calculating Minimum Horsepower Required to Drag a 350 kg Box
What minimum horsepower must a motor have to be able to drag a 350 kg box along a level floor at a speed of 1.05 m/s if the coefficient of friction is 0.40?
A) 2.94 hp
B) 3.78 hp
C) 4.12 hp
D) 5.25 hp
Final Answer:
To determine the minimum horsepower needed to drag a 350 kg box along a level floor at a speed of 1.05 m/s, calculate the force of friction using the coefficient of friction and the weight of the box, and then calculate the minimum horsepower required using the formula for horsepower.
Answer:
The correct answer is not provided in the options. Therefore, none of the given options are correct for this question.
To determine the minimum horsepower needed to drag a 350 kg box along a level floor at a speed of 1.05 m/s, we first need to calculate the force of friction. The equation for friction is f = μN, where μ is the coefficient of friction and N is the normal force.
The normal force is equal to the weight of the box, which is given by N = mg, where m is the mass and g is the acceleration due to gravity. Using the coefficient of friction provided (0.40), the weight of the box (350 kg × 9.8 m/s²), and the formula for horsepower (HP = F × v ÷ 745.7), we can calculate the minimum horsepower required.
First, calculate the normal force:
N = 350 kg × 9.8 m/s² = 3430 N
Then, calculate the force of friction:
f = 0.40 × 3430 N = 1372 N
Finally, calculate the minimum horsepower required:
HP = (1372 N × 1.05 m/s) ÷ 745.7 = 1.94 hp
The correct answer is not provided in the options. Therefore, none of the given options are correct for this question.