Physics 2000 JAMB Past Questions - Question 11: A rope is being used to pull a mass of 10 kg vertically upward. Determine the tension in the rope if, starting from rest, the mass acquires a velocity of 4ms-¹ in 8s.

Correct Answer

D

Explanation

To determine the tension in the rope, you can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the mass is 10 kg, and the acceleration can be determined from the change in velocity over time.To determine the tension in the rope, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

Given:
Mass (m) = 10 kg
Initial velocity (u) = 0 m/s (starting from rest)
Final velocity (v) = 4 m/s
Time (t) = 8 s

First, we can calculate the acceleration (a) using the equation:

a = (v - u) / t

a = (4 m/s - 0 m/s) / 8 s
a = 0.5 m/s²

Next, we can calculate the net force (F) acting on the mass using Newton's second law:

F = m * a

F = 10 kg * 0.5 m/s²
F = 5 N

Since the rope is pulling the mass vertically upward, the tension in the rope is equal to the net force acting on the mass. Therefore, the tension in the rope is 5 N.

The initial velocity (u) is 0 m/s (starting from rest), and the final velocity (v) is 4 m/s. The time (t) is 8 seconds.

First, calculate the acceleration (a):

a = (v - u) / t
a = (4 m/s - 0 m/s) / 8 s
a = 0.5 m/s²

Now that you have the acceleration, you can calculate the tension in the rope using Newton's second law:

F = m * a

where F is the force (tension in the rope), m is the mass (10 kg), and a is the acceleration (0.5 m/s²).

F = 10 kg * 0.5 m/s²
F = 5 N

So, the tension in the rope is 5 Newtons.