Answer:
W = 0.63 KJ
Explanation:
Work (W) is defined as the point product of force (F) by the distance (d)the body travels due to this force.
W= F*d *cosα Formula (1)
F : force (N)
d : displacement (m)
α : angle between force and displacement
Newton's second law:
∑F = m*a Formula (2)
∑F : algebraic sum of the forces in Newton (N)
m : mass s (kg)
a : acceleration (m/s²)
We define the x-axis in the direction parallel to the movement of the cart on the ramp and the y-axis in the direction perpendicular to it.
Forces acting on the cart
W: Weight of the cart : In vertical direction
FN : Normal force : perpendicular to the floor
f : Friction force: parallel to the floor
T : tension Force, inclined at θ=24.7° above the horizontal
Calculated of the W
W= m*g
W= 9.13 kg* 9.8 m/s² = 89.47 N
x-y components o the tension force (T)
Tx = Tcosθ = T*cos 24.7° (N)
Ty = Tsin θ = T*sin 24.7° (N)
Calculated of the FN
We apply the formula (2)
∑Fy = m*ay ay = 0
FN +Ty- W = 0
FN = W-Ty
FN = 89.47-T*sin 24.7°
Calculated of the friction force (f)
f = μk*FN
f =(0.597)*( 89.47-T*sin 24.7°
)
f= 53.41-0.249T
Calculated of the tension force of the rope (f)
We apply the formula (2) :
∑Fx = m*ax , ax= 0 ,because the speed of the cart is constant
Tx - f = 0
T*cos 24.7°-( 53.41 - 0.249T )= 0
T*cos 24.7° + 0.249T = 53.41
(1.1575)T = 53.41
T= (53.41) / (1.1575)
T= 46.14 N
Work done on the cart by the rope
We apply the formula (1)
W=T*d *cosα
W= (46.14 N)*(15.1 m) *(cos24.7)
W = 632.97 (N*m) = 632.97 (J)
W = 0.63 KJ
= characteristic wavelength = 9 μm = 9 x 10⁻⁹ m