Which sentence uses commas correctly? Carl could rope ride and herd for the ranch. Carl could rope, ride, and herd for the ranch.

# Tag: rope

Marcus has a rope that was 75 feet long. He cut off part of the rope. After that the rope was 56 feet long. If f= the number of feet marcus cut off the rope, which mathematical sentence expresses the information above a) 75-f=56 b)75-f>56 c) f-75>56 d) f-75_56

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a.) Applying Newton’s 2nd law: F= ma

Summation of forces along the y-direction:

F = 0 (objects at rest)

N + Wy = 0

N + 68(9.81)(sin 22) = 0

N = 250 Newtons

Summation of forces along the x-direction

F = 0

f + F + 68(9.81)(cos 22) = 0

The frictional force’s formula is f = ∪s*N (if at rest) = ∪k*N (if moving)

where ∪ is the coefficient of friction (s for static and k for kinetic)

Thus, the equation becomes

0.5(N) + F + 68(9.81)(cos 22) = 0

0.5(250) + F + 68(9.81)(cos 22) = 0**F = 743.45 Newtons**

b.) Same procedure but only differs in f = ∪k*N, where ∪k = 0.35. Then,0.35(N) + F + 68(9.81)(cos 22) = ma (for objects moving)

0.35(250) + 743.45 + 68(9.81)(cos 22) = 68(a)

**a = 21.32 m/s^2**

What must the students’ muscles do to pull the rope