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(1)Sphere A is attached to the ceiling of an elevator by astring. A second sphere is attached to the first one by a secondstring. Both strings are of negligible mass. Herem₁ = m₂ = m = 3.57kg.

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

(b) If the elevator moves upward instead with the sameacceleration what will be the tension in the two strings innewtons?

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

(2) Consider the 65.0-kg ice skater being pushed by two othersshown 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 bythe others, given that the magnitudes F₁ andF₂ are 22.0 N and 15.8 N, respectively.(AssumeF₁points in the positivex direction.)

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

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

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

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

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

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