If both the external and internal forces are conservative/ derivative from potentials, then show that the total potential energy V of the system is expressed as N N V v = 2V + ±Σ Σ V ΣV i ij i i=1j=ii#j
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![If both the external and internal forces are conservative/ derivative from
potentials, then show that the total potential energy V of the system is
expressed as
N
N
V- ΣV , + Σ Σ ν,
ij
i=1j=i i+j
i](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf940ef5-f11d-47b6-8c22-c10e6083c392%2F30aaac40-6d50-43c5-b441-bb306b1e7242%2Fs9sfcjh_processed.jpeg&w=3840&q=75)
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- Please asapWhat amount of work that need to be done by an external force on a particle on a frictionless, horizontal surface to double its speed from v to 2v? equal to the work required to accelerate the object from v = 0 to v, twice the work required to accelerate the object from v = 0 to v, three times the work required to accelerate the object from v = 0 to v, four times the work required to accelerate the object from 0 to v, or not known without knowledge of the acceleration?How much power is needed to lift a 750 kg elephant 14.3 m in 30.0 seconds? Paragraph V B I U A/ Ev + v
- Needs Complete typed solution with 100 % accuracy.A 5.58 kg object falls freely (ignore air resistance), after being dropped from rest. Determine the initial kinetic energy (in J), the final kinetic energy (in J), and the change in kinetic energy (in J) for the following. (a) the first meter of the fall initial kinetic energy final kinetic energy change in kinetic energy initial kinetic energy final kinetic energy (b) the second meter of the fall 0 X How is the initial kinetic energy for the second segment of travel related to the final kinetic energy for the first segment of travel? J change in kinetic energy 0 J J J 54.684 54.684 X How is the final kinetic energy related to the change in kinetic energy? J 109.368 X Can you determine the change in gravitational potential energy for the object as it falls during the second segment of travel? How is the change in kinetic energy for the second segment of travel related to the change in potential energy for the second segment? J 109.368 X Knowing the initial kinetic energy and the change…Why is the work done by a conservative force the negative of the change in potential energy? The equation for the work done is W = q∆V = -∆PE.
- 1. Boxing gloves are padded to lessen the force of a blow. The glove and face compress 7.5000 cm during a blow in which the 7.0000-kg arm and glove are brought to rest from an initial speed of 10.0000 m/s. ▬▬ - Think & Prepare 1. Make note of what's given and what's unknown. Relate known quantities to symbols. 2. Draw a labeled sketch if possible. 3. Identify the physics principle and approach. Write down relevant equations symbolically. Simplify if possible. 4. Insert numerical quantities to solve for unknowns. 5. Does the answer make sense? % (a) Calculate the change in kinetic energy of the glove and arm. AKE = (b) Where does this energy go? O Search 5 O into doing work against the force exerted by the face against the glove O into doing work against gravity O into the potential energy of the face O into the potential energy of the glove and arm T 4- 6 Y 17 + & J 7 90 8 * 8 U I 이 144 ( 9 110 DII O E DDI I P 2 { 4 ( ← backsA 5.56 kg object falls freely (ignore air resistance), after being dropped from rest. Determine the initial kinetic energy (in J), the final kinetic energy (in J), and the change in kinetic energy (in J) for the following. (a) the first meter of the fall initial kinetic energy ____J final kinetic energy _____J change in kinetic energy ____J (b) the second meter of the fall initial kinetic energy ____J final kinetic energy _____J change in kinetic energy _____JA spring with k = 15 N/m with equilibrium length 30 cm is attached vertically to a surface and then allowed to come to equilibrium, after which a weight with mass 0.2 kg is attached to the top side of the spring. → How much work does the Earth do on the weight via gravity between its initial position and the new equilibrium height? Explicitly compute the work with an integral.
- show workA particle moves along a curved path y(x) = (10 m){1+cos[(0.1 m−1)x]} , from x = 0 to x = 10π m, subject to a tangential force of variable magnitude F(x) = (10 N)sin[(0.1 m−1)x]. How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)You stand at the top of a cliff and lower a first aid kit (attached to a rope) down the cliff to an injured hiker at a constant speed. What can you say about the work done by the rope and the work done by gravity on the kit as it is lowered? O The work done by the rope is positive and the work done by gravity is positive. The work done by the rope is negative and the work done by gravity is negative. O The work done by the rope is positive and the work done by gravity is negative. O The work done by the rope is zero and the work done by gravity is zero. O The work done by the rope is negative and the work done by gravity is positive.