It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/s. A 60 kg passenger gets aboard on the ground floor. What is the passengers

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Himin1945 · Accepted Answer

Step 1  Given values:  m=60 kg  t=4s  v2=10ms  a) The elevator is at rest. The only two forces acting are gravitational and the forece of the normal reaction of the substrate.  Step 2  N=mg  N=60kg⋅(9.81ms2)  N=588.6 N  W=588.6  Step 3  b) We eill find the acceleration of the elevator from the equation:  v2=v1+at  v1=0ms  v2=at  a=v2t  a=10ms4s  a=2.5ms2  ⇒N=m(a+g)  N=60kg⋅(9.81ms2+2.5ms2)  N=60kg⋅(12.31ms2)  N=738.6 N  Step 4  c) When the elevator reaches maximum speed, it no longer accelerates.  a=0ms2  F=ma  0=N−mg  N=mg  N=60kg⋅(9.81ms2)  Answer:  a) N=588.6 N  b) N=738.6 N  c) N=588.6 N

Volosoyx · Accepted Answer

Step 1  Concepts and reason  The concepts required to solve the problem are the fundamental kinematic equation of motion for velocity and Newton’s second law of motion.  To calculate the apparent weight, use Newton’s second law of motion. Use the kinematic equation for velocity of the elevator and calculate the acceleration from the equation. Use the acceleration to calculate the apparent weight.  Fundamentals According to the fundamental kinematic equation of motion, the final velocity of an object is  v=u+at  Here, v is the final velocity of the object, u is the initial velocity of the object, a is the acceleration of the object and t is the time.  According to Newton’s second law, the force acting on an object is:  F=ma  Here, F is the force, m is the mass of the object and a is the acceleration of the object.  The weight of an object under acceleration due to gravity is:  W=mg  Here, W is the weight of the object, m is the mass of the object, and g is the acceleration due to gravity.  The apparent weight of the passenger before the elevator starts moving is:  W=mg  Step 2  Substitute 60 kg for m and 9.8ms2 for g to calculate the apparent weight of the passenger.  W=(60kg)(9.8ms2)  =588 N  According to the fundamental kinematic equation of motion, the final velocity of the passenger is,  v=u+at  Since the passenger starts from rest, the initial velocity of the passenger will be zero.  u=0  Substitute 0 for u in the equation v=u+at and solve for a.  v=0+at  a=vt  The net force acting on the passenger when he is moving upward is:  F=Wa−W  Here, F is the net force on the passenger, W is the weight of the passenger under acceleration due to gravity, and Wa is the apparent weight of the passenger when the elevator moves upward.  According to Newton’s second law of motion, the net force acting on the passenger is,  F=ma  Substitute vt for a in the above expression to rewrite F.  F=mvt  The weight of the passenger under acceleration due to gravity is,  W=mg  Rewrite the equation for net force F=Wa−W in terms of apparent weight of the passenger.  The apparent weight of the passenger is,  Wa=F+W  Step 3  Substitute mvt for F and mg for W in Wa=F+W in the above expression to rewrite Wa  Wa=mvt+mg  =m(vt+g)  Substitute 60 kg for m, 10ms for v, 4.0s for t, and 9.8ms2 for acceleration due to gravity to calculate Wa  Wa=(60kg)(10ms4.0s+9.8ms2)  =738N The apparent weight of the passenger while the elevator is speeding up is 738 N.  Step 4  When the elevator reaches the cruising speed, the elevator stops accelerating upward and moves with the constant speed. The only acceleration acting on the passenger is the acceleration due to gravity.  The apparent weight of the passenger is,  W=mg  Substitute 60 kg for m and 9.9ms2 for g to calculate the apparent weight of the passenger.  W=(60kg)(9.8ms2)  =588 N  The apparent weight of the passenger after the elevator reaches the cruising speed is 588N  Ans:  The apparent weight of the passenger before the elevator starts moving is588N  The apparent weight of the passenger while the elevator is speeding up is 738N  The apparent weight of the passenger after the elevator reaches the cruising speed is 588N

Nick Camelot · Accepted Answer

Answer:150NExplanation:The force acting on an object can be determined using Newton&#039;s second law of motion, which states that the force (F) is equal to the mass (m) of the object multiplied by its acceleration (a). In this case, the acceleration is the rate at which the elevator reaches its cruising speed.The formula to calculate acceleration is given by:a=vf−vitwhere a is the acceleration, vf is the final velocity (cruising speed), vi is the initial velocity (zero in this case), and t is the time taken to reach the cruising speed.Given that vf=10m/s and t=4.0s, we can calculate the acceleration:a=10m/s−04.0s=2.5m/s2Now, we can calculate the force experienced by the passenger using Newton&#039;s second law:F=m·aGiven that the mass of the passenger is m=60kg, we can substitute the values:F=60kg·2.5m/s2=150NTherefore, the force experienced by the passenger when the elevator reaches its cruising speed is 150N.

madeleinejames20 · Accepted Answer

1. Calculate the force required to accelerate the elevator:The force required can be calculated using Newton&#039;s second law of motion: F=m·a, where m is the mass of the passenger and a is the acceleration. Since the elevator takes 4.0 s to reach its cruising speed, the acceleration can be calculated as: a=vt, where v is the cruising speed (10 m/s) and t is the time taken to reach that speed (4.0 s).2. Calculate the force exerted on the passenger:The force exerted on the passenger is equal to the weight of the passenger, which can be calculated using the formula: Fweight=m·g, where m is the mass of the passenger and g is the acceleration due to gravity (approximately 9.8 m/s2).3. Compare the forces:If the force required to accelerate the elevator is greater than the force exerted on the passenger, the passenger will experience an upward force and will feel lighter. If the force required is less than the force exerted on the passenger, the passenger will experience a downward force and will feel heavier.

Mr Solver · Accepted Answer

Step 1: Calculate the force required to accelerate the elevator.Step 2: Use Newton&#039;s second law to find the acceleration.Step 3: Determine the distance traveled during the acceleration phase.Step 4: Calculate the time taken to reach cruising speed.Step 5: Calculate the work done during the acceleration phase.Step 6: Calculate the potential energy gained by the passenger.Step 7: Calculate the final answer.Let&#039;s start with Step 1:Step 1: Calculate the force required to accelerate the elevator.The force required to accelerate an object is given by Newton&#039;s second law: F=ma, where F is the force, m is the mass, and a is the acceleration.In this case, the mass of the passenger is 60 kg, and the acceleration is what we need to find. So we can rewrite the equation as: F=(60kg)(a).Step 2: Use Newton&#039;s second law to find the acceleration.We know that the force required to accelerate the elevator is equal to the weight of the passenger. The weight of an object is given by W=mg, where W is the weight, m is the mass, and g is the acceleration due to gravity.In this case, W=(60kg)(9.8m/s2)=588N.Setting the force equal to the weight, we have F=W=588N.Substituting this into the equation from Step 1, we get: 588N=(60kg)(a).Solving for a, we have: a=588N60kg=9.8m/s2.Step 3: Determine the distance traveled during the acceleration phase.To find the distance traveled during the acceleration phase, we can use the equation: d=12at2, where d is the distance, a is the acceleration, and t is the time.In this case, the time is 4.0 seconds, and the acceleration is 9.8 m/s^2. Substituting these values into the equation, we get: d=12(9.8m/s2)(4.0s)2=78.4m.Step 4: Calculate the time taken to reach cruising speed.The time taken to reach cruising speed can be calculated by dividing the distance traveled during the acceleration phase by the cruising speed. In this case, the distance is 78.4 m and the cruising speed is 10 m/s.So, the time taken to reach cruising speed is: t=dv=78.4m10m/s=7.84s.Step 5: Calculate the work done during the acceleration phase.The work done during the acceleration phase can be calculated using the equation: W=Fd, where W is the work, F is the force, and d is the distance.In this case, the force is the weight of the passenger (588 N) and the distance is the distance traveled during the acceleration phase (78.4 m).So, the work done during the acceleration phase is: W=(588N)(78.4m)=46099.2J.Step 6: Calculate the potential energy gained by the passenger.The potential energy gained by the passenger can be calculated using the equation: PE=mgh, where PE is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.In this case, the mass is 60 kg, the acceleration due to gravity is 9.8 m/s^2, and the height is the distance traveled during the acceleration phase (78.4 m).So, the potential energy gained by the passenger is: PE=(60kg)(9.8m/s2)(78.4m)=45619.2J.Step 7: Calculate the final answer.To find the passenger&#039;s kinetic energy when the elevator reaches its cruising speed, we subtract the potential energy gained from the work done during the acceleration phase.The kinetic energy is given by: KE=W−PE=46099.2J−45619.2J=480J.Therefore, the passenger&#039;s kinetic energy when the elevator reaches its cruising speed is 480 J.

It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/

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