Question

A crate of oranges with a total mass of 6.7 kg is being pulled across a skating rink (frictionless) with a rope that makes an angle of 0.7 rad above the horizontal. John, who measures the motion of the crate, sees that it accelerates at a constant rate of 4.2 m/s2. What is the tension in the rope in N?

Answer 1

The tension in the rope is 36.792 N

Step-by-step explanation:

Data given:

m = 6.7 kg

θ = 0.7 rad = 40.107°

a = acceleration = 4.2 m/s²

The tension in the rope is:

`T=(ma)/(cos\theta ) =(6.7*4.2)/(cos40.107) =36.792N`

Answer 2

36.74 N

Step-by-step explanation:

Given that:

A crate of oranges with a total mass (m) = 6.7 kg

angle θ = 0.7 rad

angle θ =
`0.7 * (180)/(\pi)`

angle θ = 40°

acceleration = 4.2 m/s²

Given that:

T cosθ = ma

T cos 40° = 6.7 × 4.2

T =
`\frac { 6.7 * 4.2}{cos \ 40}`

T =
`\frac { 28.14}{0.7660}`

T = 36.74 N

Thus, the tension in the rope = 36.74 N