a block of mass 10kg is kept on ground. a vertically upward force F=(20t)N starts acting at t=0. the height of the block from the ground at t=10s is
To find the height of the block from the ground at t = 10s, we need to integrate the force with respect to time to find the work done on the block and then use that to calculate the change in potential energy.
The force acting on the block is given by F = 20t N, where t is the time in seconds.
The work done on the block is equal to the integral of the force with respect to time. We can find the work done by integrating the force function over the interval t = 0 to t = 10.
∫(20t) dt = 10t² [from t = 0 to t = 10]
= (10 * 10²) - (10 * 0²)
= 1000 - 0
= 1000 J (Joules)
The work done on the block is 1000 Joules.
The change in potential energy of the block is equal to the negative of the work done on the block. This is because as the block moves upward, the work done on the block is stored as potential energy.
Change in potential energy (ΔPE) = -1000 J (since the work done is positive)
The change in potential energy can be calculated using the formula:
ΔPE = mgh
Where m is the mass of the block, g is the acceleration due to gravity, and h is the height change.
Given that the mass of the block is 10 kg and g is approximately 9.8 m/s² (acceleration due to gravity), we can rearrange the formula to solve for h:
h = ΔPE / (mg)
h = (-1000 J) / (10 kg * 9.8 m/s²)
h = -10.2 m
The negative sign indicates that the block has moved down by 10.2 meters from its starting position. Therefore, the height of the block from the ground at t = 10s is -10.2 meters.