A cord is used to lower vertically a block of 10 kg by a distance of 2 mwith a constant acceleration of 2.5 ms2. Calculate the work done by the cord on the block.
Question
A cord is used to lower vertically a block of 10 kg by a distance of 2 mwith a constant acceleration of 2.5 ms2. Calculate the work done by the cord on the block.
Solution
To calculate the work done by the cord on the block, we need to know the force exerted by the cord and the distance over which it is applied.
Step 1: Calculate the force exerted by the cord.
The force exerted by the cord is equal to the difference between the weight of the block and the force due to its acceleration.
The weight of the block (W) can be calculated using the formula W = m*g, where m is the mass of the block and g is the acceleration due to gravity.
In this case, m = 10 kg and g = 9.8 m/s^2 (approximate value), so W = 10 kg * 9.8 m/s^2 = 98 N.
The force due to the block's acceleration (F) can be calculated using the formula F = m*a, where m is the mass of the block and a is its acceleration.
In this case, m = 10 kg and a = 2.5 m/s^2, so F = 10 kg * 2.5 m/s^2 = 25 N.
The force exerted by the cord (Fc) is therefore Fc = W - F = 98 N - 25 N = 73 N.
Step 2: Calculate the work done by the cord.
The work done by the cord (Wc) can be calculated using the formula Wc = Fc * d, where Fc is the force exerted by the cord and d is the distance over which it is applied.
In this case, Fc = 73 N and d = 2 m, so Wc = 73 N * 2 m = 146 J.
Therefore, the work done by the cord on the block is 146 J.
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