Problem 4: The Slingshot is a ride for two people. It consists of a single passenger cage, two towers, and two elastic bands. Potential energy is stored in the elastic bands and the passenger cage is released. On the way up, this potential energy in the elastic bands is converted into the kinetic energy of the cage. At the maximum height of the ride, the energy has been converted into gravitational potential energy of the cage. The slingshot has two towers of height h = 75 m. The towers are a distance d = 32 m apart. Each elastic band has an unstretched length of Lo = 41 m and a spring constant of k = M. 295 N/m. The total mass of the passengers and cage is m = 395 kg. The car is pulled down to the ground in the middle of the two towers. h Part (a) Write an expression for the stretched length L of one of the elastic bands strung from the cage to the top of its tower. MultipleChoice : 1) (h² + d² )!/2 2) h? + d? 3) (h? + (d/2)² )\/2 4) h? + (d/2)? 5) (h? + d² )/2 - Lo 6) (h? + (d/2)2 )/2 - Lo Part (b) Calculate the stretched length, in meters, of each band. Numeric : A numeric value is expected and not an expression. L = Part (c) Write an expression for the total potential energy stored in the elastic bands before the cage is released. MultipleChoice : 1) k (h? + (d/2)2 ) 2) k ( h? + (d/2)²)2 3) k ( (h? + (d/2)² )2 - Lo )? 4) k (h? + (d/2)² - Lo )? 5) k/2 (h? + (d/2)² ) 6) k/2 ( (h? + (d/2)² )2 - Lo)?
Problem 4: The Slingshot is a ride for two people. It consists of a single passenger cage, two towers, and two elastic bands. Potential energy is stored in the elastic bands and the passenger cage is released. On the way up, this potential energy in the elastic bands is converted into the kinetic energy of the cage. At the maximum height of the ride, the energy has been converted into gravitational potential energy of the cage. The slingshot has two towers of height h = 75 m. The towers are a distance d = 32 m apart. Each elastic band has an unstretched length of Lo = 41 m and a spring constant of k = M. 295 N/m. The total mass of the passengers and cage is m = 395 kg. The car is pulled down to the ground in the middle of the two towers. h Part (a) Write an expression for the stretched length L of one of the elastic bands strung from the cage to the top of its tower. MultipleChoice : 1) (h² + d² )!/2 2) h? + d? 3) (h? + (d/2)² )\/2 4) h? + (d/2)? 5) (h? + d² )/2 - Lo 6) (h? + (d/2)2 )/2 - Lo Part (b) Calculate the stretched length, in meters, of each band. Numeric : A numeric value is expected and not an expression. L = Part (c) Write an expression for the total potential energy stored in the elastic bands before the cage is released. MultipleChoice : 1) k (h? + (d/2)2 ) 2) k ( h? + (d/2)²)2 3) k ( (h? + (d/2)² )2 - Lo )? 4) k (h? + (d/2)² - Lo )? 5) k/2 (h? + (d/2)² ) 6) k/2 ( (h? + (d/2)² )2 - Lo)?
Transcribed Image Text:Problem 4: The Slingshot is a ride for two people. It consists of a single passenger
cage, two towers, and two elastic bands. Potential energy is stored in the elastic bands
and the passenger cage is released. On the way up, this potential energy in the elastic
bands is converted into the kinetic energy of the cage. At the maximum height of the
ride, the energy has been converted into gravitational potential energy of the cage. The
slingshot has two towers of height h = 75 m. The towers are a distance d = 32 m apart.
Each elastic band has an unstretched length of Lo = 41 m and a spring constant of k =
295 N/m. The total mass of the passengers and cage is m = 395 kg. The car is pulled
down to the ground in the middle of the two towers.
MŨ
Part (a) Write an expression for the stretched length L of one of the elastic bands strung from the cage to the top of its tower.
MultipleChoice :
1) (h² + d² )!/2
2) h² + d²
3) ( h² + (d/2)² )/2
4) h? + (d/2)?
5) ( h2 + d² )'/2 - Lo
6) ( h? + (d/2)? )1/2 - Lo
Part (b) Calculate the stretched length, in meters, of each band.
Numeric : A numeric value is expected and not an expression.
L =
Part (c) Write an expression for the total potential energy stored in the elastic bands before the cage is released.
MultipleChoice :
1) k ( h² + (d/2)² )
2) k ( h? + (d/2)2)2
3) k ( (h² + (d/2)2 )2 - Lo )²
4) k ( h? + (d/2)² - Lo)²
5) k/2 ( h² + (d/2)? )
6) k/2 ( (h² + (d/2)² )!12 - Lo )²
Part (d) Calculate the total potential energy, in joules, stored in the elastic bands before the cage is released.
Numeric : A numeric value is expected and not an expression.
U =
Part (e) Calculate the maximum height, in meters, of the ride.
Numeric : A numeric value is expected and not an expression.
hf =.
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