Question

Consider the 65.0 kg ice skater being pushed by two others shown in the figure. 

(a) Find the direction (in degrees) and magnitude (in N) of F_tot, the total force exerted on her by the others, given that the magnitudes F₁ and F₂ are 27.2 N and 18.2 N, respectively. 

(b) What is her initial acceleration (in m/s²) if she is initially stationary and wearing steel-bladed skates that point in the direction of F_tot? 

(c) What is her acceleration (in m/s²) assuming she is already moving in the direction of F_tot? Remember that friction is always in the opposite direction of motion or attempted motion between surfaces in contact. 

Answer 1

a) given that

forces F1 = 27.2 N

F2 = 18.2 N

magnitude F = sqrt(F1^2+F2^2)

F = sqrt(27.2^2+18.2^2)

F = 32.73 N

direction = tan^-1(18.2/27.2) = 33.79 degrees from the force F1

b) given mass m = 65 kg

Ftot-friction = ma

a = 1/m(32.73-$\mu s$*mg)

$\mu s$ = 0.04 for ice surface

acceleration a = 1/65*(32.73-0.04*65*9.8)

a = 0.11 m/s^2

c) a = 1/65*(32.73-0.02*65*9.8)

a = 0.307 m/s^2