A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if
a. The box is at rest?
b. The box moves at a steady 5.0 m/s?
c. The box has v_x = 5.0 m/s and a_x = 5.0 m/s^2?

Respuesta :

Answer:

A

B

C

Explanation:

A)

The tension is 0 because there is no net force.

B)

The tension is once again 0 because the acceleration is 0 which means there is no net force.

C)

Ma=F

50 kg x 5 m/s^2=F

250 N= F

Answer:

a. 0 N

b. 0 N

c. 250 N

Explanation:

(a) If the box is at rest, that means that there is no acceleration since the net force acting on the block is 0.

We know that the acceleration must be 0 m/s², so by using Newton's 2nd Law:

  • F = ma

We can calculate the tension force since we have the mass and acceleration of the box.

  • F_T = ma
  • F_T = (50 kg)(0 m/s²)
  • F_T = 0 N

The force of tension in the rope is 0 N if the box is at rest.

(b) If the box is moving at a constant velocity, this means that there are no unbalanced forces acting on the box. Therefore, since the net force is 0 the acceleration is also 0 m/s².

Since this is the same scenario as before, we know that the tension in the rope is 0 N if the box moves at a constant velocity of 5.0 m/s.

(c) Now we are given the acceleration of the box, so we can calculate the tension force using Newton's 2nd Law:

  • F_T = ma
  • F_T = (50 kg)(5.0 m/s²)
  • F_T = 250 N

The tension in the rope if the box has an acceleration of 5.0 m/s² is 250 N. Notice that the velocity does not affect the force.