A5.8kg box is on a frictionless 45∘ slope and is connected via a massless string over a massless, frictionless pulley to a hanging 2.1kg weight. what is the tension in the string if the 5.8kg box is held in place, so that it cannot move? what is the tension in the string once the box begins to move?

a) T = 20.601 N

b) T = 9.4585 N

Step-by-step explanation:

The tension in the string if the 5.8 kg box is held in place, so that it cannot move can be obtained as follows

For m = 2.1 Kg

∑ Fy = 0

T - W = 0  ⇒  T = W = m*g

⇒  T = 2.1 Kg*9.81 m/s²

⇒  T = 20.601 N  (↑)

The tension in the string once the box begins to move can be obtained as follows

For M = 5.8 Kg

∑ Fx' = M*a

where x' is the direction of the slope

then

∑ Fx' = M*a   ⇒  T - M*g*Sin ∅ = M*a    (I)

For m = 2.1 Kg

∑ Fy = m*a

⇒  T - W = m*a

⇒  T - m*g = m*a    (II)

If we solve the system of equations that comprises I and II we will know T:

T = M*m*g*(Sin ∅ -1) / (m - M)

⇒  T = (5.8 Kg)(2.1 Kg)(9.81 m/s²)(Sin 45º - 1) / (2.1 Kg - 5.8 Kg)

⇒  T = 9.4585 N

b is the final answer! : )

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.