A block of mass 10 kg is suspended by an inextensible string passing over a smooth frictionless pulley. If the mass is pulled up at an acceleration of 1 m/s², calculate the tension in the string.
Question
A block of mass 10 kg is suspended by an inextensible string passing over a smooth frictionless pulley. If the mass is pulled up at an acceleration of 1 m/s², calculate the tension in the string.
Solution
To calculate the tension in the string, we can use Newton's second law of motion.
Step 1: Identify the forces acting on the block. In this case, we have the force of gravity acting downwards (weight) and the tension in the string acting upwards.
Step 2: Determine the acceleration of the block. In this case, the block is being pulled up with an acceleration of 1 m/s².
Step 3: Use Newton's second law to relate the net force to the mass and acceleration. The net force is equal to the difference between the weight and the tension in the string. So we have:
Net force = mass * acceleration
Step 4: Calculate the weight of the block. The weight is given by the formula:
Weight = mass * gravitational acceleration
In this case, the mass of the block is 10 kg and the gravitational acceleration is approximately 9.8 m/s².
Weight = 10 kg * 9.8 m/s² = 98 N
Step 5: Substitute the values into the equation from step 3:
Net force = 98 N - Tension
10 kg * 1 m/s² = 98 N - Tension
Step 6: Solve for the tension in the string:
Tension = 98 N - 10 kg * 1 m/s²
Tension = 98 N - 10 N
Tension = 88 N
Therefore, the tension in the string is 88 N.
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