Question

(1)Sphere A is attached to the ceiling of an elevator by a string. A second sphere is attached to the first one by a second string. Both strings are of negligible mass. Here m₁ = m₂ = m = 3.57 kg.

(a) The elevator starts from rest and accelerates downward witha= 1.35 m/s². What are the tensions in the two strings in newtons?

(b) If the elevator moves upward instead with the same acceleration what will be the tension in the two strings in newtons?

(c)The maximum tension the two strings can withstand is 92.2 N. What maximum upward acceleration (in m/s²) can the elevator have without having one of the strings break?

(2) Consider the 65.0-kg ice skater being pushed by two others shown in the figure below.

(a)Find the direction (in degrees counterclockwise from the +x-axis) and magnitude (in N) ofF_totthe total force exerted on her by the others, given that the magnitudes F₁ and F₂ are 22.0 N and 15.8 N, respectively. (AssumeF₁points in the positive x direction.)

(b) What is her initial acceleration (in m/s²) if she is initially stationary and wearing steel-bladed skates that point in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(c) What is her acceleration (in m/s²) assuming she is already moving in the direction ofF_tot?(Assume friction is negligible. Enter the magnitude only.)

(3)Here, m_A = 2.50 kg and m_B = 6.50 kg. The string connecting the two objects is of negligible mass and the pulley is frictionless. The objects start from rest and move with constant acceleration.

(a) What is the magnitude of the acceleration (in m/s²) of each of the objects?

(b) What is the magnitude (in N) of the tension in the string?

(c)Through what distance (in m) will the two objects move in the first three seconds of motion?

Answer 1