The catapult from part (a) is undergoing testing. The spring constant of the elastic band in the catapult is 92 N m−1. In one test the band is extended by 0.3 m.
(b)
Calculate the elastic potential energy stored in the elastic band of the catapult.
A new type of pushchair for dolls is being developed. In one round of testing a pushchair has a force of 20 N applied for a distance of 5 m at an angle of 45° to the horizontal.
At an athletics training camp, runners are being tested for their speed, efficiency and power. A runner with a mass of 52 kg manages to maintain a constant velocity of 7 m s−1.
Astronauts are in training for a planned mission to land on the surface of Jupiter.
(a)
Identify, by placing a tick (✔) in the box(es), which of the following tasks will be more difficult to carry out due to the larger acceleration of free fall on Jupiter.
A ball is dropped from a height of 2 m towards the surface of Jupiter. The acceleration of free fall on Jupiter is 24.58 m s−2.
(b)
Calculate the speed of the ball just as it hits the surface. Assume that no energy is lost to the surroundings.
(i)
State the relationship, in symbols, between gravitational potential energy at the point the ball is dropped from and the kinetic energy just before it hits the surface
[1]
(ii)
Rearrange the relationship found in part (i) to obtain an equation for v, the speed of the ball when it hits the surface
Astronauts have developed special tents with stiff springs to erect on the surface of Jupiter. The springs hang freely vertically with one end fixed to the tent and the other with a mass secured.
(d)
Label the diagram below to show the spring when the gravitational potential energy (ΔEp), kinetic energy (Ek) and elastic potential energy (Ep) are each at their maximum.
A violin maker is conducting materials testing on various new strings. The first string has a spring constant of 23 000 N m−1 and is extended by 0.06 m before it breaks.
(a)
Calculate the force applied to the string just before it breaks.
