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Three boxes are attached together with ropes having tensions T₁ and T2, as shown in the figure below. The masses of the boxes are mA = 22.4 kg, mB = 18.3 kg and mc = 25.5 kg. A force of 400 N is applied to Box C at an angle of 0 = 35 deg. A) Find the tensions in each rope. B) Calculate the acceleration of the system. C) What new force (also at angle 35 deg) would be required to keep the system moving to the right with constant speed? Assume that the coefficients of kinetic friction for each box are μA = 0.38, μв = 0.46, and pc = 0.32, respectively.

Three boxes are attached together with ropes having tensions T₁ and T2, as shown in the figure below. The masses of the boxes are mA = 22.4 kg, mB = 18.3 kg and mc = 25.5 kg. A force of 400 N is applied to Box C at an angle of 0 = 35 deg. A) Find the tensions in each rope. B) Calculate the acceleration of the system. C) What new force (also at angle 35 deg) would be required to keep the system moving to the right with constant speed? Assume that the coefficients of kinetic friction for each box are μA = 0.38, μв = 0.46, and pc = 0.32, respectively.

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**Problem Statement:** Three boxes are attached together with ropes having tensions \( T_1 \) and \( T_2 \), as shown in the figure below. The masses of the boxes are \( m_A = 22.4 \, \text{kg} \), \( m_B = 18.3 \, \text{kg} \), and \( m_C = 25.5 \, \text{kg} \). A force of 400 N is applied to Box C at an angle of \( \theta = 35^\circ \). **Tasks:** 1. Find the tensions in each rope. 2. Calculate the acceleration of the system. 3. What new force (also at angle \( 35^\circ \)) would be required to keep the system moving to the right with constant speed? **Note:** Assume that the coefficients of kinetic friction for each box are \( \mu_A = 0.38 \), \( \mu_B = 0.46 \), and \( \mu_C = 0.32 \), respectively. **Diagram:** - Box A (colored in red) is on the left, connected by a rope with tension \( T_1 \) to Box B. - Box B (colored in blue) is in the middle, connected by a rope with tension \( T_2 \) to Box C. - Box C (colored in green) is on the right, with the applied force \( F \) at an angle \( \theta = 35^\circ \). - The force \( F \) acts diagonally upwards to the right.
Transcribed Image Text:**Problem Statement:** Three boxes are attached together with ropes having tensions \( T_1 \) and \( T_2 \), as shown in the figure below. The masses of the boxes are \( m_A = 22.4 \, \text{kg} \), \( m_B = 18.3 \, \text{kg} \), and \( m_C = 25.5 \, \text{kg} \). A force of 400 N is applied to Box C at an angle of \( \theta = 35^\circ \). **Tasks:** 1. Find the tensions in each rope. 2. Calculate the acceleration of the system. 3. What new force (also at angle \( 35^\circ \)) would be required to keep the system moving to the right with constant speed? **Note:** Assume that the coefficients of kinetic friction for each box are \( \mu_A = 0.38 \), \( \mu_B = 0.46 \), and \( \mu_C = 0.32 \), respectively. **Diagram:** - Box A (colored in red) is on the left, connected by a rope with tension \( T_1 \) to Box B. - Box B (colored in blue) is in the middle, connected by a rope with tension \( T_2 \) to Box C. - Box C (colored in green) is on the right, with the applied force \( F \) at an angle \( \theta = 35^\circ \). - The force \( F \) acts diagonally upwards to the right.
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