A mountain rescue team is preparing to move a stretcher (with an injured climber) down a flat slope. The combined mass of the stretcher and climber is 85 kg, and the slope makes an angle of 18◦ with the horizontal. The stretcher is held in place by a rope that makes an angle of 25◦ with the slope. The stretcher is on the point of slipping down the slope. The coefficient of static friction between the slope and the stretcher is 0.15. stretcher 18◦ 25◦ rope Model the stretcher and climber as a particle, the slope as a plane and the rope as a model string. Take the magnitude of the acceleration due to gravity to be g = 9.8 m s−2, and round your answers to two significant figures. (a) Draw a force diagram showing the four forces acting on the stretcher. Define the symbols that you use to denote the forces. Choose the Cartesian unit vector i to be parallel to and pointing up the slope, and the Cartesian unit vector j to be perpendicular to the slope and pointing upwards. Mark these vectors on your diagram. [8] (b) Express the forces in component form, in terms of unknown magnitudes where appropriate. Hence determine the magnitude (in newtons) of the tension in the rope.
You should be able to answer this question after studying Unit 5.
A mountain rescue team is preparing to move a stretcher (with an injured
climber) down a flat slope. The combined mass of the stretcher and climber
is 85 kg, and the slope makes an angle of 18◦ with the horizontal. The
stretcher is held in place by a rope that makes an angle of 25◦ with the slope.
The stretcher is on the point of slipping down the slope. The coefficient of
static friction between the slope and the stretcher is 0.15.
stretcher
18◦
25◦
rope
Model the stretcher and climber as a particle, the slope as a plane and the
rope as a model string. Take the magnitude of the acceleration due to gravity
to be g = 9.8 m s−2, and round your answers to two significant figures.
(a) Draw a force diagram showing the four forces acting on the stretcher.
Define the symbols that you use to denote the forces.
Choose the Cartesian unit vector i to be parallel to and pointing up the
slope, and the Cartesian unit vector j to be perpendicular to the slope
and pointing upwards. Mark these vectors on your diagram. [8]
(b) Express the forces in component form, in terms of unknown magnitudes
where appropriate. Hence determine the magnitude (in newtons) of the
tension in the rope.
Step by step
Solved in 5 steps with 3 images
