A box is pushed with a force of 50 N on a surface with a coefficient of kinetic friction of 0.4. What is the acceleration of the box if its mass is 10 kg?
Practice Questions
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Q1
A box is pushed with a force of 50 N on a surface with a coefficient of kinetic friction of 0.4. What is the acceleration of the box if its mass is 10 kg?
1 m/s²
2 m/s²
3 m/s²
4 m/s²
Net force = applied force - frictional force. Frictional force = μ_k * N = 0.4 * 10 kg * 9.8 m/s² = 39.2 N. Net force = 50 N - 39.2 N = 10.8 N. Acceleration = F/m = 10.8 N / 10 kg = 1.08 m/s², approximately 1 m/s².
Questions & Step-by-step Solutions
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Q
Q: A box is pushed with a force of 50 N on a surface with a coefficient of kinetic friction of 0.4. What is the acceleration of the box if its mass is 10 kg?
Solution: Net force = applied force - frictional force. Frictional force = μ_k * N = 0.4 * 10 kg * 9.8 m/s² = 39.2 N. Net force = 50 N - 39.2 N = 10.8 N. Acceleration = F/m = 10.8 N / 10 kg = 1.08 m/s², approximately 1 m/s².
Steps: 7
Step 1: Identify the applied force on the box, which is 50 N.
Step 2: Determine the mass of the box, which is 10 kg.
Step 3: Calculate the weight of the box using the formula: Weight (N) = mass (kg) * gravity (m/s²). Here, gravity is approximately 9.8 m/s². So, Weight = 10 kg * 9.8 m/s² = 98 N.
Step 4: Find the normal force (N), which is equal to the weight of the box. Therefore, N = 98 N.
Step 5: Calculate the frictional force using the formula: Frictional force = coefficient of kinetic friction (μ_k) * normal force (N). Here, μ_k = 0.4, so Frictional force = 0.4 * 98 N = 39.2 N.
Step 6: Calculate the net force acting on the box using the formula: Net force = applied force - frictional force. So, Net force = 50 N - 39.2 N = 10.8 N.
Step 7: Finally, calculate the acceleration of the box using the formula: Acceleration (a) = Net force (N) / mass (kg). So, a = 10.8 N / 10 kg = 1.08 m/s².
