A push cart of mass 200 kg is loaded with vegetables of 50 kg initially. A vegetable vendor pushed the cart to the maximum and made it to accelerate by 2m/s22m/s 2 . He sold all the vegetables and on his way home, he pushed the empty cart to the maximum and made it to accelerate. Find the acceleration of the empty push cart.
Question
A push cart of mass 200 kg is loaded with vegetables of 50 kg initially. A vegetable vendor pushed the cart to the maximum and made it to accelerate by 2m/s22m/s 2 . He sold all the vegetables and on his way home, he pushed the empty cart to the maximum and made it to accelerate. Find the acceleration of the empty push cart.
Solution
Sure, let's solve the problem step by step.
Given: Mass of the push cart (m1) = 200 kg Mass of the loaded vegetables (m2) = 50 kg Acceleration of the loaded push cart (a1) = 2 m/s^2
To find: Acceleration of the empty push cart (a2)
Step 1: Calculate the total mass of the loaded push cart. Total mass (m) = m1 + m2 = 200 kg + 50 kg = 250 kg
Step 2: Use Newton's second law of motion to find the force applied to the loaded push cart. Force (F1) = m * a1 = 250 kg * 2 m/s^2 = 500 N
Step 3: When the vegetables are sold, the mass of the push cart becomes equal to the mass of the empty push cart (m1). So, the force applied to the empty push cart (F2) is the same as F1.
Step 4: Use Newton's second law of motion to find the acceleration of the empty push cart. F2 = m1 * a2 500 N = 200 kg * a2
Step 5: Solve for a2. a2 = 500 N / 200 kg a2 = 2.5 m/s^2
Therefore, the acceleration of the empty push cart is 2.5 m/s^2.
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