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# A rope is being used to pull a mass of 10kg vertically upward. Determine the ten...

### Question

A rope is being used to pull a mass of 10kg vertically upward. Determine the tension in the rope if, starting from rest, the mass acquires a velocity of 4ms-1 in 8s [g = 10ms-2]

### Options

A)
5N
B)
50N
C)
95N D)
105N

### Explanation:

First, we need to find the acceleration of the mass. We can use the formula:

$$v = u + at$$

Where $$v$$ is the final velocity, $$u$$ is the initial velocity, $$a$$ is the acceleration, and $$t$$ is the time taken. In this case, the mass starts from rest, so $$u = 0$$. The final velocity is given as $$v = 4ms^{-1}$$, and the time taken is $$t = 8s$$.

Substituting the values into the equation, we get:

$$4 = 0 + a(8)$$

Now, we can solve for the acceleration:

$$a = \frac{4}{8} = 0.5ms^{-2}$$

Next, we need to find the net force acting on the mass. This can be calculated using Newton's second law:

$$F_{net} = ma$$

Where $$F_{net}$$ is the net force, $$m$$ is the mass, and $$a$$ is the acceleration. We have the values for mass $$m = 10kg$$ and acceleration $$a = 0.5ms^{-2}$$, so we can calculate the net force:

$$F_{net} = 10 \times 0.5 = 5N$$

Now, we need to find the gravitational force acting on the mass, which is given by:

$$F_g = mg$$

Where $$F_g$$ is the gravitational force, $$m$$ is the mass, and $$g$$ is the acceleration due to gravity. We have the given value of $$g = 10ms^{-2}$$. Substituting the values, we get:

$$F_g = 10 \times 10 = 100N$$

Finally, we need to find the tension in the rope, which is the force required to balance the gravitational force and provide the net force. The tension can be calculated using the equation:

$$T = F_g - F_{net}$$

Substituting the values we found earlier, we get:

$$T = 100 - 5 = 95N$$

Therefore, the tension in the rope is 95N, which corresponds to Option C.