Using the definition of momentum, pvector = mvvector, Newton\'s laws can be expr
ID: 1520154 • Letter: U
Question
Using the definition of momentum, pvector = mvvector, Newton's laws can be expressed in the form J_1vector + J_2vector +. .. = deltaPvector, where J_ivector = sigmaF_ivector deltat is the impulse due to force F_ivector. When a ball of mass m_1 = 1.00kg is falling (on Earth of mass m_2 = 5.97times 10^24 kg) what are the individual accelerations of the ball and Earth? A student of mass m = 60.0 kg jumps off a table at height h = 1.00m. While hitting the floor he bends his knees such that the time of contact is 100.0 ms. What is the new force exerted by the floor now? A drop of rain and a pellet of hail, of the same mass m = 1.00g, hits the roof of a car with the same speed v = 5.00m/s. Rain drop being liquid stays in contact with the roof for 100.0ms, while hail being solid rebounds (assume with same speed v = 5.00 m/s) and that stays in contact for a mere 1.00ms. Calculate the force exerted by each on the roof of the car. (The numbers quoted here are based on reasonable guesses, and could be off by an Older of magnitude.)Explanation / Answer
The impact interval for the rain drop is dT and for the hail it's dt < dT. This results because the water collapses over the length of the drop, while the stone shatters, which is an immediate response.
So the respective impact forces are f = m dV/dT and F = m dV/dt where m = 10^-3 kg and dV = 5 m/s the decrease in speed over the intervals of time.
dT = 100 ms = 0.1 sec
dt = 1 ms = 10^-3 sec
Therefore, f = m dV/dT = 10^-3 * 5 / 0.1 = 0.05 N due to rain drop
F = m dV/dt = 10^-3 * 5 / 10^-3 = 5 N due to hai
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