How Do Friction and Tension Forces Affect Motion?

[Kimorto]

Question #1) A boy pulls a sled of mass 5.0 kg with a rope that makes an 60.0degree angle with respect to the horizontal surface of a frozen pond. The boy pulls on the rope with a force of 10.0 N; and the sled moves with constant velocity. What is the coefficient of friction between the sled and the ice.

My answer: 10 * Cos 60 = 5 = Ff
5 * 9.80 = 49 = Fn
5 / 49 = .102
.102 = coefficient of friction (My answer)
.12 = (Teacher answer)

Question #2) A rock is suspended from a string; and it accelerates downward. Which one of the following statements concerning the tension in the string is true?
A) The tension points downward
B) The tension is less that the weight of the rock
C) The tension is equal to the weight of the rock.
D) The tension is greater that the weight of the rock.
E) The tension is independant of the magnitude of the rock's acceleration.

The answer is B, and I don't know why. Please help explain.

 

[HallsofIvy]

The tension in the string is the force pulling up on the rock. The weight of the rock is the force pulling down. You are told that the rock acclerates downward. What does that tell you about the net force?

 

[wais]

The correct answer is C) The tension is equal to the weight of the rock. This is because according to Newton's second law, the net force on an object is equal to its mass multiplied by its acceleration. In this case, the only forces acting on the rock are its weight (due to gravity) and the tension in the string. Since the rock is accelerating downward, the tension in the string must be equal to its weight in order to balance out the downward force and keep the rock suspended. If the tension were less than the weight of the rock, the rock would accelerate downward at a faster rate. If the tension were greater than the weight of the rock, the rock would accelerate upward. Therefore, the tension must be equal to the weight of the rock in order to maintain a constant downward acceleration.