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

Answer:

The tension in the rope is 36.792 N

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:

$T=\frac{ma}{cos\theta } =\frac{6.7*4.2}{cos40.107} =36.792N$

Answer 2

Answer:

36.74 N

Explanation:

Given that:

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

angle θ = 0.7 rad

angle θ = $0.7 * \frac{180}{\pi}$

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