Answer each problem carefully.1. A person bicycling uses 100N of force at a distance traveled of50m. How much work is done by the person.2. An acrobat weighs 45kg and suspended 3m in air. How much isher potential energy?3. A 47kg ballet dancer leaps across the floor at 1 m/s. How muchkinetic energy does she have?4. A 10kg box has a potential energy of 2000 J. How high is itsuspended?5. A 50kg ice skater glides on the ice with a velocity 10 m/s,backwards. What is her kinetic energy?
Answer (1)
Answer:Let's solve each problem step by step: Problem 1: Given: - Force = 100 N- Distance traveled = 50 m Work Done = Force x DistanceWork Done = 100 N x 50 mWork Done = 5000 Joules Therefore, the work done by the person is 5000 Joules. Problem 2: Given: - Mass of the acrobat = 45 kg- Height = 3 m- Acceleration due to gravity = 9.81 m/s^2 Potential Energy = Mass x Gravity x HeightPotential Energy = 45 kg x 9.81 m/s^2 x 3 mPotential Energy = 1320.15 Joules Therefore, the potential energy of the acrobat is 1320.15 Joules. Problem 3: Given: - Mass of the ballet dancer = 47 kg- Velocity = 1 m/s Kinetic Energy = 0.5 x Mass x Velocity^2Kinetic Energy = 0.5 x 47 kg x (1 m/s)^2Kinetic Energy = 23.5 Joules Therefore, the kinetic energy of the ballet dancer is 23.5 Joules. Problem 4: Given: - Mass of the box = 10 kg- Potential Energy = 2000 J- Acceleration due to gravity = 9.81 m/s^2 Potential Energy = Mass x Gravity x Height2000 J = 10 kg x 9.81 m/s^2 x HeightHeight = 2000 J / (10 kg x 9.81 m/s^2)Height ≈ 20.4 meters Therefore, the box is suspended at a height of approximately 20.4 meters. Problem 5: Given: - Mass of the ice skater = 50 kg- Velocity = 10 m/s Kinetic Energy = 0.5 x Mass x Velocity^2Kinetic Energy = 0.5 x 50 kg x (10 m/s)^2Kinetic Energy = 2500 Joules Therefore, the kinetic energy of the ice skater is 2500 Joules.
