Two masses, 5 kg and 7 kg, are connected by a string over a frictionless pulley. Calculate the acceleration of the masses and the tension in the string.

Question

Asked on April 27, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-04-27T02:21:38.132Z

Hey Adeyemi — ready when you are. Here are the steps to solve the problem: a) Find acceleration Step 1: Identify the masses and set up Newton's second law for each mass. Let m_1 = 5 \, kg and m_2 = 7 \, kg. Since m_2 > m_1, m_2 accelerates downwards and m_1 accelerates upwards. Let a be the magnitude of the acceleration and T be the tension in the string. We use g = 9.8 \, m/s^2. For m_1 (moving upwards): T - m_1 g = m_1 a (1) For m_2 (moving downwards): m_2 g - T = m_2 a (2) Step 2: Add the two equations to eliminate T and solve for a. (T - m_1 g) + (m_2 g - T) = m_1 a + m_2 a m_2 g - m_1 g = (m_1 + m_2) a a = ((m_2 - m_1)g)/(m_1 + m_2) Step 3: Substitute the given values into the acceleration formula. a = (7 \, kg - 5 \, kg)(9.8 \, m/s^2)5 \, kg + 7 \, kg a = (2 \, kg)(9.8 \, m/s^2)12 \, kg a = 19.6 \, m/s^212 a ≈ 1.63 \, m/s^2 The acceleration is 1.63 m/s^2. b) Find T, the tension in the string Step 1: Use one of the original equations (Equation 1 or Equation 2) and the calculated acceleration to find the tension T. Using Equation 1: T = m_1 g + m_1 a T = m_1 (g + a) Step 2: Substitute the values for m_1, g, and a. T = 5 \, kg (9.8 \, m/s^2 + 1.6333... \, m/s^2) T = 5 \, kg (11.4333... \, m/s^2) T ≈ 57.2 \, N The tension in the string is 57.2 N. c) Find force ceiling must exert on pulley Step 1: Analyze the forces acting on the pulley. The string exerts a downward force equal to the tension T on each side of the pulley. Therefore, the total downward force exerted by the string on the pulley is 2T. The ceiling must exert an upward force F_c to support the pulley. Assuming the pulley is massless and in equilibrium (not accelerating vertically), the upward force from the ceiling must balance the total downward force from the string. F_c = 2T Step 2: Substitute the calculated tension T. F_c = 2 × 57.1666... \, N F_c ≈ 114 \, N The force the ceiling must exert on the pulley is 114 N. Send me the next one 📸

Accepted Answer · 2026-04-27T02:21:38.132Z

Hey Adeyemi — ready when you are. Here are the steps to solve the problem: a) Find acceleration Step 1: Identify the masses and set up Newton's second law for each mass. Let m_1 = 5 \, kg and m_2 = 7 \, kg. Since m_2 > m_1, m_2 accelerates downwards and m_1 accelerates upwards. Let a be the magnitude of the acceleration and T be the tension in the string. We use g = 9.8 \, m/s^2. For m_1 (moving upwards): T - m_1 g = m_1 a (1) For m_2 (moving downwards): m_2 g - T = m_2 a (2) Step 2: Add the two equations to eliminate T and solve for a. (T - m_1 g) + (m_2 g - T) = m_1 a + m_2 a m_2 g - m_1 g = (m_1 + m_2) a a = ((m_2 - m_1)g)/(m_1 + m_2) Step 3: Substitute the given values into the acceleration formula. a = (7 \, kg - 5 \, kg)(9.8 \, m/s^2)5 \, kg + 7 \, kg a = (2 \, kg)(9.8 \, m/s^2)12 \, kg a = 19.6 \, m/s^212 a ≈ 1.63 \, m/s^2 The acceleration is 1.63 m/s^2. b) Find T, the tension in the string Step 1: Use one of the original equations (Equation 1 or Equation 2) and the calculated acceleration to find the tension T. Using Equation 1: T = m_1 g + m_1 a T = m_1 (g + a) Step 2: Substitute the values for m_1, g, and a. T = 5 \, kg (9.8 \, m/s^2 + 1.6333... \, m/s^2) T = 5 \, kg (11.4333... \, m/s^2) T ≈ 57.2 \, N The tension in the string is 57.2 N. c) Find force ceiling must exert on pulley Step 1: Analyze the forces acting on the pulley. The string exerts a downward force equal to the tension T on each side of the pulley. Therefore, the total downward force exerted by the string on the pulley is 2T. The ceiling must exert an upward force F_c to support the pulley. Assuming the pulley is massless and in equilibrium (not accelerating vertically), the upward force from the ceiling must balance the total downward force from the string. F_c = 2T Step 2: Substitute the calculated tension T. F_c = 2 × 57.1666... \, N F_c ≈ 114 \, N The force the ceiling must exert on the pulley is 114 N. Send me the next one 📸

Two masses, 5 kg and 7 kg, are connected by a string over a frictionless pulley. Calculate the acceleration of the masses and the tension in the string.

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Two masses, 5 kg and 7 kg, are connected by a string over a frictionless pulley. Calculate the acceleration of the masses and the tension in the string.

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