A box of mass 5.8 kg with initial speed 7.2 m s–1 begins to move up a smooth incline.
The box is momentarily brought to rest after colliding with a spring of spring constant 210 N m–1. It stops a vertical distance of 0.65 m above its initial position.
(a)
(i)
Calculate the initial energy of the box
(ii)
Determine an equation for the final energy of the box when it collides with the spring
There is now a constant frictional force of 16 N opposing the motion of the box as it moves along the slope uphill part of its path. The incline is at an angle of 22º from the horizontal.
(c)
Calculate the magnitude of the work done on the box as it travels uphill.
Some cargo ships use kites working together with the ship’s engines to move the vessel.
The tension in the cable that connects the kite to the ship is 350 kN. The kite is pulling the ship at an angle of θ to the horizontal. The ship travels at a steady speed of 3.9 m s–1 when the ship’s engines operate with a power output of 5.7 MW.
(a)
Calculate the angle θ if the work done on the ship by the kite when the ship travels for 5 minutes, before the engines are cut off, is 355 MJ.
The kite is taken down and no longer produces a force on the ship. The resistive force F that opposes the motion of the ship is related to the speed v of the ship by
F = kv
where k is a constant.
(d)
Show that, if the power output of the engines remains at 5.7 MW, the speed of the ship will decrease to about 3.5 m s–1. Assume that k is independent of whether the kite is in use or not.
Question 3a
Marks: 3
The arrangement shown below is used to test golf club heads.
The shaft of a club is pivoted and the centre of mass of the club head is raised by a height h before being released. The club head then falls back to the vertical position where it strikes the ball.
(a)
Calculate the maximum speed of the club head achieved when h = 75 cm.
The optimal launch angle for a projectile, such as a golf ball, is 45º. Another experiment is carried out with a golf club that has a shaft 1.14 m long.
(c)
Calculate the maximum speed this club head achieves just before it hits the ball.
Explain why the power of the motor is only a minimum.
Question 4c
Marks: 3
A different motor is used to lift an identical mass through the same distance in the same amount of time with an overall efficiency of 38 %. The mass experiences a resistive force of 170 N.
The car engine cuts off whilst travelling up the incline.
(c)
Assuming there are no resistive forces, calculate the distance travelled by the car from when the engine cuts off to when it has a gravitational potential energy of 110 kJ.
