To determine the tension in the rope when pulling a mass of 10 kg vertically upward, we need to consider both the force required to overcome gravity and the force required to accelerate the mass. Let's break this down step-by-step. ### Step 1: Identify the Forces Acting on the Mass When pulling the mass upward, two main forces are acting on it: 1. **Weight of the mass (W)**: This is the force due to gravity acting downward. 2. **Tension in the rope (T)**: This is the force exerted by the rope acting upward. The weight of the mass can be calculated using the formula: \[ W = m \cdot g \] where: - \( m = 10 \, \text{kg} \) (mass) - \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity) Calculating the weight: \[ W = 10 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 100 \, \text{N} \] ### Step 2: Calculate the Acceleration of the Mass Next, we need to find the acceleration of the mass as it is pulled upward. We know that the mass starts from rest and reaches a velocity of \( 4 \, \text{m/s} \) in \( 8 \, \text{s} \). We can use the formula for acceleration (\( a \)): \[ a = \frac{\Delta v}{\Delta t} \] where: - \( \Delta v = 4 \, \text{m/s} - 0 \, \text{m/s} = 4 \, \text{m/s} \) - \( \Delta t = 8 \, \text{s} \) Calculating the acceleration: \[ a = \frac{4 \, \text{m/s}}{8 \, \text{s}} = 0.5 \, \text{m/s}^2 \] ### Step 3: Apply Newton's Second Law According to Newton's second law, the net force (\( F_{\text{net}} \)) acting on the mass is equal to the mass times its acceleration: \[ F_{\text{net}} = m \cdot a \] Calculating the net force: \[ F_{\text{net}} = 10 \, \text{kg} \cdot 0.5 \, \text{m/s}^2 = 5 \, \text{N} \] ### Step 4: Determine the Tension in the Rope The net force acting on the mass is also the difference between the tension in the rope and the weight of the mass: \[ F_{\text{net}} = T - W \] Rearranging this gives us: \[ T = F_{\text{net}} + W \] Substituting the values we calculated: \[ T = 5 \, \text{N} + 100 \, \text{N} = 105 \, \text{N} \] ### Conclusion Thus, the tension in the rope is **105 N**. ### Explanation of Other Options - **Option A (5 N)**: This option only considers the net force due to acceleration and ignores the weight of the mass. It is incorrect because it does not account for the force needed to overcome gravity. - **Option B (50 N)**: This option is also incorrect as it seems to miscalculate the forces involved. It does not consider the full weight of the mass and the additional force required for acceleration. - **Option C (95 N)**: This option incorrectly assumes that the tension is just slightly less than the weight of the mass, which would imply a downward acceleration. It does not account for the upward acceleration correctly. ### Revision Summary - The weight of the mass is calculated using \( W = m \cdot g \). - Acceleration is found using \( a = \frac{\Delta v}{\Delta t} \). - The net force is determined using \( F_{\text{net}} = m \cdot a \). - Tension in the rope is calculated as \( T = F_{\text{net}} + W \). This thorough understanding of forces and motion is crucial for solving similar problems in physics.